A363922 - OEIS

%I #46 Sep 27 2023 02:42:56

%S 1,2,1,1,2,1,-1,2,1,1,3,1,1,-1,1,1,2,2,1,6,-1,1,2,2,1,2,1,-1,48,1,1,5,

%T 1,1,-1,1,10,2,1,12,2,-1,3,3,1,1,3,1,-1,2,8,7,3,1,1,-1,1,1,9,1,1,2,-1,

%U 1,2,5,1,3,2,-1,2,1,66,2,1,3,-1,1,1,3

%N a(n) = smallest number m > 0 such that n followed by m 7's yields a prime, or -1 if no such m exists.

%C a(n) = -1 when n = 7*k because no matter how many 7's are appended to n, the resulting number is always divisible by 7 and therefore cannot be prime.

%C a(n) = -1 when n = 15873*k + 891, 1261, 2889, 3263, 3300, 7810, 8917, 9812, 12617, 13024, 14615 or 15066, because n followed by any positive number, m say, of 7's is divisible by at least one of the primes {3,11,13,37}.

%C Similarly,

%C a(n) = -1 when n = 11111111*k + 964146, 1207525, 2342974, 3567630, 7525789, 8134540, 8591231 or 9641467 by primes {11,73,101,137};

%C a(n) = -1 when n = 429000429*k + 23928593, 27079312, 36492115, 41207969, 52285750, 80569929, 89920882, 93857078, 133928703, 217208145, 223492302, 236849444, 239285937, 247857232, 259793116, 270793127, 323985244, 332698824, 333570182, 334985255, 346849554, 364921157, 376698868 or 412079697 by primes {3,11,13,101,9901};

%C a(n) = -1 when n = 1221001221*k + 14569863, 28792885, 145698637, 167698659, 225079510, 235985156, 247079532, 287928857, 331921124, 399492478, 415286113, 421492500, 437286135, 455985376, 489857474, 529929099, 551921344, 635208563, 709857694, 877208805, 896850104, 993570842, 1029793886 or 1138850346 by primes {3,11,37,101,9901};

%C a(n) = -1 when n = 1443001443*k + 85928655, 167698659, 176928746, 218921011, 233985154, 247079532, 310492389, 326286024, 376857361, 585793442, 655208583, 700699192, 746208674, 780080065, 791570640, 805850013, 843492922, 859286557, 882570731, 896850104, 1027793884, 1219922012, 1234986155 or 1377858362 by primes {3,13,37,101,9901}.

%C a(4444) > 300000 or a(4444) = -1.

%H Toshitaka Suzuki, <a href="/A363922/b363922.txt">Table of n, a(n) for n = 1..4443</a>

%e a(11)=3 because 117 and 1177 are composite but 11777 is prime.

%o (PARI) a(n) = if ((n%7), my(m=1); while (!isprime(eval(concat(Str(n), Str(7*(10^m-1)/9)))), m++); m, -1); \\ _Michel Marcus_, Jul 17 2023

%Y Cf. A008589, A069568, A090464, A113076.

%K sign,base

%O 1,2

%A _Toshitaka Suzuki_, Jul 12 2023