------------------------------------------------------------------------------------------------ Primzahlen in den Folgen mit leerem Präfix oder leerem Suffix; angegeben werden die n so dass a(n) prim ist. Die nur aus Präfix oder Postfix bestehende Zahl hat Index 0, die Zahl aus Präfix und einer Kernziffer oder Suffix und einer Kernziffer hat Index 1, usw. Zusammenstellung der zur Zeit (26. Oktober 2004) in der On-Line Encyclopedia of Integer Sequences (maintained by N.J.A. Sloane) enthaltenen Folgen; alle Folgen sind bis mindestens zum Index 5000 untersucht worden. Durch # abgetrennt sind weitere nicht unbedingt konsekutive Terme. Zu jeder Folge wird ein durch Primteiler mit kleiner Periode gebildetes Sieb angegeben, das die Möglichkeiten weiterer Primzahlen beschränkt. Zusätzlich ggf. OEIS-Einträge mit evtl. anderem Anfang und um 1 oder 2 erhöhten Index. ------------------------------------------------------------------------------------------------ Teil 1: Folgen mit leerem Präfix ------------------------------------------------------------------------------------------------ Form s,c A-Nummer Terme ------------------------------------------------------------------------------------------------ 11..11 0,1 A004023 2,19,23,317,1031,49081,86453 prim höchstens für n=[1, 7, 11, 13, 17, 19, 23, 29] mod 30, sonst teilbar durch [11, 3, 41] 11..13 3,-17 A056654 0,1,2,4,8,10,23,83,220,1313,2951 prim höchstens für n=[2, 4, 5] mod 6, sonst teilbar durch [3, 13] A097683 0,1,2,3,5,9,11,24,84,221,1314,2952 11..17 7,-53 A056655 0,1,3,4,7,22,28,39,130,135,214,610,766,2152,2575 prim höchstens für n=[1, 3, 4, 7, 9, 10, 13, 15, 16, 19, 21, 22, 25, 28] mod 30, sonst teilbar durch [3, 7, 31] A097684 1,2,4,5,8,23,29,40,131,136,215,611,767,2153,2576 11..19 9,-71 A056659 1,4,5,7,16,49,683,719,1451,1678,3145 prim höchstens für n=[1, 4, 5] mod 6, sonst teilbar durch [3, 7] A097685 2,5,6,8,17,50,684,720,1452,1679,3146 22..21 1,11 A056660 3,17,99,120,243,545,630,1493,2565 prim höchstens für n=[0, 3, 5] mod 6, sonst teilbar durch [3, 13] A084832 4,18,100,121,244,546,631,1494,2566 22..23 3,-7 A056656 0,1,2,7,10,35,94,100,127,259,350,466,644,1010,1177,1216,2441,3760,3805 prim höchstens für n=[1,2,4,5,7,8,10,11,13,14,16,17,19,20,23,25,26,28, 29,31,32,34,35,37,40,41,43,44,46,47] mod 48, sonst teilbar durch [3,17] A096506 1,2,3,8,11,36,95,101,128,260,351,467,645,1011,1178,1217,2442,3761,3806 22..27 7,-43 A056677 0,2,8,14,27,63,1167,1694,2361 prim höchstens für n=[2, 3, 5, 8, 9, 14, 15, 17, 20, 21, 23, 26, 27, 29, 33, 35, 38, 41] mod 42, sonst teilbar durch [3, 7, 239] A099409 1,3,9,15,28,64,1168,1695,2362 22..29 9,-61 A056678 1,2,4,13,175,415,2504,2758 prim höchstens für n=[1, 2, 4] mod 6, sonst teilbar durch [3, 7] A099410 2,3,5,14,176,416,2505,2759 33..31 1,21 A055520 1,2,3,4,5,6,7,17,39,49,59,77,100,150,318,381,783,1731,1917,8854,11244, 11959,12129,18532,22717,23364,24252,24548,25323,30177 prim höchstens für n=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14] mod 15, sonst teilbar durch [31] A055557 2,3,4,5,6,7,8,18,40,50,60,78,101,151,319,382,784,1732,1918,8855,11245, 11960,12130,18533,22718,23365,24253,24549,25324,30178 33..37 7,-33 A056680 0,1,2,5,45,393,977,2585,2810,2967,3641,4826,4917,5591,5705 prim höchstens für n=[2, 3, 5] mod 6, sonst teilbar durch [37, 7] A099411 1,2,3,6,46,394,978,2586,2811,2968,3642,4827,4918,5592,5706 44..41 1,31 A056681 1,3,10,27,54,93,474,2079,4834,5844 prim höchstens für n=[0, 3, 4, 7, 9, 10, 12, 13] mod 15, sonst teilbar durch [3, 41] A099412 0,2,4,11,28,55,94,475,2080,4835,5845 44..43 3,13 A056661 0,1,2,5,8,11,29,31,182,296,491 prim höchstens für n=[1,2,5,8,11,13,14,17,19,20,25,26,29,31,32,35,37, 38,41,43,44,47] mod 48, sonst teilbar durch [3, 7, 17] A096845 1,2,3,6,9,12,30,32,183,297,492 44..47 7,-23 A056682 0,1,3,9,19,25,721,1309,3169 prim höchstens für n=[1, 3] mod 6, sonst teilbar durch [3, 7, 13] A099413 0,1,2,4,10,20,26,722,1310,3170 44..49 9,-41 A056683 2,4,5,47,107,244,1043 prim höchstens für n=[2,4,5,8,10,11,14,16,17,20,22,23,26,29,32,34,35, 38,40,41,46,47] mod 48, sonst teilbar durch [3, 7, 17] A099414 0,3,5,6,48,108,245,1044 55..51 1,41 A056684 11,12,608 prim höchstens für n=[0, 2, 6, 8, 11, 12, 14, 17, 18, 23, 24, 26, 29] mod 30, sonst teilbar durch [3, 7, 31] A099415 12,13,609 55..53 3,23 A056685 0,1,7,25,65,73,232,472,539,2773 prim höchstens für n=[1, 5, 7, 10, 11, 13, 16, 17, 19, 22, 23] mod 24, sonst teilbar durch [3, 7, 73] A099416 0,1,2,8,26,66,74,233,473,540,2774 55..57 7,-13 A056686 0,2,3,5,9,14,21,87,206,527,959,2099 prim höchstens für n=[2, 3, 5, 9, 11, 14, 15, 17, 20, 21, 26, 27, 29] mod 30, sonst teilbar durch [3, 7, 31] A099417 0,1,3,4,6,10,15,22,88,207,528,960,2100 55..59 9,-31 A056687 1,7,11,17,25,31,137,187,221,337,1001,2743 prim höchstens für n=[1,5,7,11,13,17,19,23,25,29,31,37,41,43,47,49,53, 55,59,65,67,71,73,77] mod 78, sonst teilbar durch [3, 7, 13, 53] A099418 2,8,12,18,26,32,138,188,222,338,1002,2744 66..61 1,51 A056658 1,2,3,9,17,20,21,27,42,65,120,132,177,240,453,552,1599,2174,2977,3648 prim höchstens für n=[0, 1, 2, 3, 5, 6, 7, 9, 11, 12, 13, 14, 15, 17] mod 18, sonst teilbar durch [7, 19] A098088 2,3,4,10,18,21,22,28,43,66,121,133,178,241,454,553,1600,2175,2978,3649 66..67 7,-3 A056657 0,1,5,7,8,10,19,22,40,62,65,118,121,148,251,283,304,591,745,874,1203, 1363,2239,2402,5105,5775,5812,12455,14234 prim höchstens für n=[1, 2, 3, 4, 5] mod 6, sonst teilbar durch [7] A096507 1,2,6,8,9,11,20,23,41,63,66,119,122,149,252,284,305,592,746,875,1204, 1364,2240,2403,5106,5776,5813,12456,14235 77..71 1,61 A056688 1,12,19,22,30,99,240,274,924,1066,1368,2064 prim höchstens für n=[0,1,3,4,6,9,10,12,13,15,16,18,19,21,22,24,25,27, 28,30,31,33,34,36,37,40,42,43,45,46] mod 48, sonst teilbar durch [3,17] A099419 2,13,20,23,31,100,241,275,925,1067,1369,2065 77..73 3,43 A056689 0,1,2,4,8,11,14,20,263,382,2719,4493 prim höchstens für n=[2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 19, 20, 22, 23] mod 24, sonst teilbar durch [3, 73] A099420 1,2,3,5,9,12,15,21,264,383,2720,4494 77..79 9,-11 A056693 1,65,85,89,101,385,623 prim höchstens für n=[1, 5, 8, 11, 13, 14, 19, 20, 23, 25, 26, 29] mod 30, sonst teilbar durch [3, 41, 13] A098089 2,66,86,90,102,386,624 88..81 1,71 A056664 2,18,78,138,222,462,543,1095,1418,3246,3876,4416,9506,11090,14601 prim höchstens für n=[0, 2, 3] mod 6, sonst teilbar durch [3, 7] A099421 0,3,19,79,139,223,463,544,1096,1419,3247,3877,4417,9507,11091,14602 88..83 3,53 A056694 0,1,2,4,7,8,14,50,70,76,223,295,314,2089,2905,3394,3881 prim höchstens für n=[1,2,4,5,7,8,10,13,14,16,17,19,20,22,23,25,26,28, 29,31,32,34,35,37,38,40,41,44,46,47] mod 48, sonst teilbar durch [3,17] A099422 0,1,2,3,5,8,9,15,51,71,77,224,296,315,2090,2906,3395,3882 88..87 7,17 A056695 0,2,3,5,8,11,71,117,123,189,243,303,356,1421,2690 prim höchstens für n=[2, 3, 5] mod 6, sonst teilbar durch [3, 7] A096846 1,3,4,6,9,12,72,118,124,190,244,304,357,1422,2691 88..89 9,-1 A056663 1,13,16,34,4174,4471,14575 prim höchstens für n=[1,4,5,7,10,11,13,16,17,19,22,23,28,29,31,34,35, 37,40,43,46,47] mod 48, sonst teilbar durch [3, 7, 17] A096508 2,14,17,35,4175,4472,14576 99..91 1,81 A056696 2,4,6,32,44,104,196,198,280,300,316,1106,1656,3394 prim höchstens für n=[0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 26, 28, 29] mod 30, sonst teilbar durch [7, 31] A095714 3,5,7,33,45,105,197,199,281,301,317,1107,1657,3395 99..97 7,27 A056662 0,1,2,16,139,989,1886,3529,5995,13819,21872 prim höchstens für n=[1, 2, 4, 5] mod 6, sonst teilbar durch [7, 13] A089675 1,2,3,17,140,990,1887,3530,5996,13820,21873 ------------------------------------------------------------------------------------------------ Teil 2: Folgen mit leerem Suffix ------------------------------------------------------------------------------------------------ Form s,c A-Nummer Terme ------------------------------------------------------------------------------------------------ 11..11 0,1 A004023 2,19,23,317,1031,49081,86453 prim höchstens für n=[1, 7, 11, 13, 17, 19, 23, 29] mod 30, sonst teilbar durch [11, 3, 41] 13..33 1,3 A056698 1,15,41,83,95,341,551,669,989,1223,6923 prim höchstens für n=[0, 4, 5, 6, 9, 10, 11, 12, 15, 16, 17, 21, 22, 23, 24, 27, 28, 29] mod 30, sonst teilbar durch [7, 13, 31] 17..77 1,7 A089147 1,3,9,13,42,51,54,91,120,168,510,819,1071,1756,3010,4333 prim höchstens für n=[0,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27, 28,30,31,34,36,37,39,40,42,43,45,46] mod 48, sonst teilbar durch [3,17] 19..99 1,9 A002957 1,2,3,5,7,26,27,53,147,236,248,386,401,546,785,1325,1755,2906,3020, 5407,5697,5969,7517, # 15749,19233,38232,55347 prim höchstens für n=[0, 1, 2, 3, 5, 6, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 25, 26, 27, 29] mod 30, sonst teilbar durch [7, 31] 21..11 2,1 A056700 2,3,12,18,23,57,128,543,584,833,2450,2810,2873,3671,6384 prim höchstens für n=[0,2,3,5,8,9,11,12,14,15,17,18,20,21,23,24,26,27, 29,30,32,33,35,36,39,41,42,44,45,47] mod 48, sonst teilbar durch [3,17] 23..33 2,3 A056701 0,1,2,3,4,10,16,22,53,91,94,106,138,210,282,522,597,1049,2227,6459, 10582 prim höchstens für n=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14] mod 15, sonst teilbar durch [31] 27..77 2,7 A056702 0,2,3,9,15,18,36,63,114,225,405,482,1241,2018 prim höchstens für n=[0,2,3,5,6,8,9,11,12,14,15,17,18,21,23,24,26,27, 29,30,32,35,36,38] mod 39, sonst teilbar durch [3, 53] 29..99 2,9 A056703 0,1,3,6,7,19,27,43,55,207,1311, # 7050,9439,26044,33058,34507,49314 prim höchstens für n=[0, 1, 3, 4] mod 6, sonst teilbar durch [7, 13] 31..11 3,1 A056704 1,2,5,10,11,13,34,47,52,77,88,554,580,1310,1505,8537 prim höchstens für n=[1,2,5,7,8,10,11,13,14,16,19,20,22,23,25,26,28, 29,31,32,34,35,37,38] mod 39, sonst teilbar durch [3, 53] 37..77 3,7 A056705 0,1,11,17,773,18155 prim höchstens für n=[11, 17] mod 18, sonst teilbar durch [3, 37, 13, 19] 41..11 4,1 A056706 1,3,13,25,72,108,375,393,589,973 prim höchstens für n=[0, 3, 7, 9, 12, 13, 15, 18, 19, 24, 25, 27] mod 30, sonst teilbar durch [3, 41, 7] 43..33 4,3 A056707 1,2,16,31,37,55,62,172,174,197,727,1246,1752,4318,4328,4930 prim höchstens für n=[0, 1, 2, 4, 5] mod 6, sonst teilbar durch [7] 47..77 4,7 A056708 1,4,13,25,36,357,373,1041,1089,1093,1297 prim höchstens für n=[0, 1, 3, 4, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21] mod 24, sonst teilbar durch [3, 73] 49..99 4,9 A056712 2,3,4,6,14,54,210,390,594,3460, # 8072,15796,16131,29282 prim höchstens für n=[0, 2, 3, 4, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 21, 22, 23, 24, 26, 27, 28, 29] mod 30, sonst teilbar durch [7, 31] 51..11 5,1 A056713 0,5,12,15,84,144,150,1235,1727,1812,8687 prim höchstens für n=[0, 3, 5, 6, 9, 11, 12, 15, 17, 21, 23] mod 24, sonst teilbar durch [3, 7, 73] 53..33 5,3 A056714 0,1,3,13,25,49,143,419,1705 prim höchstens für n=[0, 1, 3, 5, 6, 9, 11, 13, 15, 18, 19, 21, 23, 24, 25, 29] mod 30, sonst teilbar durch [41, 7, 13] 57..77 5,7 A056715 0,2,8,14,17,18,33,35,126,183,324,344,866,992,1226,2355 prim höchstens für n=[0,2,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26, 27,30,32,33,35,36,38] mod 39, sonst teilbar durch [3, 53] 59..99 5,9 A056716 0,1,2,4,5,7,10,13,22,23,28,34,40,61,73,361,490,613,1624,2000,2994,4301, # 18668,32544,34936 prim höchstens für n=[0, 1, 2, 4, 5] mod 6, sonst teilbar durch [7] 61..11 6,1 A056717 1,5,7,25,31,112,199,533,616,718,787,1357,2779,3889,4192,7537,7945 prim höchstens für n=[1,4,5,7,10,11,13,16,17,19,22,23,25,29,31,34, 35,37,40,41,43,46,47] mod 48, sonst teilbar durch [3, 13, 17] 67..77 6,7 A056718 1,2,4,10,13,25,115,179,181,238,785,799,1193,1730,1811,1871,2116,2180 prim höchstens für n=[1,2,4,5,7,10,11,13,14,16,17,19,20,22,23,25,26,28, 29,31,32,34,35,37,38,41,43,44,46,47] mod 48, sonst teilbar durch [3,17] 71..11 7,1 A056719 0,1,7,55 prim höchstens für n=[1,4,7,10,13,16,19,22,25,31,34,37,40,43,46,49,52, 55,58,61,64,70,73,76] mod 78, sonst teilbar durch [3, 7, 13, 79] 73..33 7,3 A056720 0,1,2,3,5,53,56,343,908,1079,2204,2379 prim höchstens für n=[2, 3, 5, 7, 8, 11, 13, 14, 15, 19, 20, 21, 23] mod 24, sonst teilbar durch [7, 13, 73] 79..99 7,9 A056721 0,1,4,5,8,10,25,49,76,128,175,238,550,796,1219,2012,2846, # 11336,49808 prim höchstens für n=[1, 2, 3, 4, 5] mod 6, sonst teilbar durch [7] 81..11 8,1 A056722 2,3,26,110,141,474,902,1746,2997,3627,3788 prim höchstens für n=[0,2,3,6,8,12,14,15,18,20,21,24,26,27,30,32, 33,36,38,39,42,44,45] mod 48, sonst teilbar durch [3, 7, 17] 83..33 8,3 A056723 1,7,23,29,133,173,367,1925,3707,5765,9769 prim höchstens für n=[0, 1, 4, 5, 6, 7, 11, 12, 13, 16, 17, 18, 19, 22, 23, 24, 28, 29] mod 30, sonst teilbar durch [7, 13, 31] 87..77 8,7 A056724 2,9,15,32,38,65,123,173,257,320,326,639,719,774,902 prim höchstens für n=[0,2,3,5,6,8,9,11,14,15,17,18,20,21,23,24,26,27, 29,30,32,33,35,36,38,39,41,42,45,47] mod 48, sonst teilbar durch [3,17] 89..99 8,9 A056725 1,3,7,19,29,37,93,935, # 8415,9631,11143,41475,41917,48051 prim höchstens für n=[0, 1, 3, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29] mod 30, sonst teilbar durch [7, 31] 91..11 9,1 A056726 2,5,20,41,47,92,161,401,455 prim höchstens für n=[2, 4, 5, 10, 11, 14, 16, 17, 20, 22, 26, 28, 29] mod 30, sonst teilbar durch [3, 7, 31] 97..77 9,7 A056727 1,2,4,19,28,73,203,220,274,292,470,763,1891,3307,7007,7306,9755 prim höchstens für n=[1,2,4,5,7,8,10,11,13,16,17,19,20,22,23,25,26,28, 29,31,32,34,35,37,38,40,41,43,44,47] mod 48, sonst teilbar durch [3,17] ------------------------------------------------------------------------------------------------