A133363 Numbers m such that 1 + Sum_{k=1..m} 3*k is prime.

3, 4, 8, 11, 16, 19, 20, 23, 31, 36, 39, 44, 48, 55, 56, 68, 71, 76, 80, 83, 84, 95, 99, 103, 104, 108, 115, 116, 124, 131, 135, 139, 140, 144, 151, 156, 163, 164, 168, 171, 180, 184, 188, 191, 195, 203, 204, 215, 216, 219, 220, 223, 244, 256, 263, 268, 271, 276

Offset: 1

Author

John W. Layman, Oct 26 2007

Keywords

• nonn

Comments

It appears that the first differences of this sequence are never of the form 4k+2.

This is true, because all terms == 0 or 3 (mod 4). - Robert Israel, Mar 16 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067196, A134460.

Programs

Maple

filter:= n -> isprime((3*n^2 + 3*n + 2)/2):
select(filter, [$1..1000]); # Robert Israel, Mar 16 2025

Mathematica

Select[Range[276],PrimeQ[1+Sum[3k,{k,#}]]&] (* James C. McMahon, Mar 15 2025 *)

PARI

lista(nn) = select(n->(isprime(1+sum(k=1,n,3*k))), vector(nn, i, i)); \\ Michel Marcus, Jul 10 2014