A092519 Smallest prime a(n) such that a(n)+6n, a(n)+12n and a(n)+18n are also primes.

5, 5, 5, 59, 7, 31, 5, 5, 5, 11, 31, 7, 23, 5, 11, 5, 7, 23, 79, 29, 5, 5, 73, 29, 7, 41, 107, 43, 19, 59, 11, 37, 13, 79, 13, 11, 17, 43, 359, 23, 31, 5, 53, 19, 47, 181, 137, 23, 59, 7, 491, 127, 283, 179, 23, 11, 7, 5, 89, 7, 461, 7, 53, 139, 31, 5, 7, 13

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Example

a(5) = 7: 7+6*5 = 7+30 = 37, 7+12*5 = 7+60 = 67, and 7+18*5 = 7+90 = 97 are all prime.

Mathematica

Module[{nn=100, prs}, prs=Prime[Range[nn]]; Table[SelectFirst[prs, AllTrue[ #+6*Range[3]*n, PrimeQ]&], {n, nn/2}]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 22 2018 *)

Prog

(Magma) prs := [NthPrime(i) : i in [1..200]]; result := []; for n in [1..100] do  for p in prs do if forall{k : k in [1..3] | IsPrime(p + 6*n*k)} then  Append(~result, p); break; end if; end for; end for; result; // Vincenzo Librandi, Jul 26 2025

Crossrefs

a(1) starts sequence A023271.

Sequence in context: A216876 A019162 A024951 * A198585 A224093 A193555

Adjacent sequences: A092516 A092517 A092518 * A092520 A092521 A092522

Keyword

nonn

Author

Ray G. Opao, Apr 06 2004

Status

approved