A075718 - OEIS

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A075718

1+n+n^s is a prime, s=12.

1, 2, 14, 30, 32, 44, 65, 87, 90, 122, 134, 149, 162, 186, 189, 227, 237, 249, 255, 266, 311, 354, 366, 456, 476, 485, 561, 567, 584, 597, 605, 650, 665, 672, 689, 720, 771, 819, 884, 899, 975, 990, 1059, 1082, 1092, 1191, 1200, 1241, 1257, 1295, 1347, 1367

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OFFSET

1,2

COMMENTS

For s = 5,8,11,14,17,20,..., n_s=1+n+n^s is always composite for any n>1. Also at n=1, n_s=3 is a prime for any s. So it is interesting to consider only the cases of s =/= 5,8,11,14,17,20,... and n>1. Here i consider the case s=12 and find several first n's making n_s a prime (or a probable prime).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..2200

EXAMPLE

2 is OK because at s=12, n=2, n_s=1+n+n^s=4099 is a prime.

MATHEMATICA

Select[Range[2000], PrimeQ[1 + # + #^12] &] (* Vincenzo Librandi, Jul 28 2014 *)

PROG

(PARI) for(n=1, 1000, if(isprime(1+n+n^12), print1(n", ")))

(Magma) [n: n in [0..2000] | IsPrime(s) where s is 1+n+n^12]; // Vincenzo Librandi, Jul 28 2014

CROSSREFS

Cf. A002384, A075717, A075719.

Sequence in context: A101554 A057018 A038341 * A259710 A093794 A294561