A055469 - OEIS

A055469

Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers).

2, 7, 11, 29, 37, 67, 79, 137, 191, 211, 277, 379, 631, 821, 947, 991, 1129, 1327, 1597, 1831, 2017, 2081, 2347, 2557, 2851, 2927, 3571, 3917, 4561, 4657, 4951, 5051, 5779, 6217, 6329, 8647, 8779, 9181, 9871, 11027, 12721, 13367, 14029, 14197, 14879

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Also primes of the form (n^2 + 7)/8. - Ray Chandler, Oct 08 2005

q=2 and q=5 are the only primes values such that q+1 is a triangular number because 8q+9 is a square for 2 and 5 only. - Benoit Cloitre, Apr 05 2002

n such that A000010(n) = A000217(k). - Giovanni Teofilatto, Jan 29 2010

It is conjectured that this sequence is infinite. - Daniel Forgues, Apr 21 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A000124(A067186(n)) = (A110873(n) + 7)/8. - Ray Chandler, Oct 08 2005

MATHEMATICA

Select[Table[(n^2 + 7)/8, {n, 400}], PrimeQ] (* Ray Chandler, Oct 08 2005 *)

Select[Accumulate[Range[400]]+1, PrimeQ] (* Harvey P. Dale, May 14 2022 *)

PROG

(PARI) forprime(p=2, 10^5, if ( issquare(8*p-7), print1(p, ", "))) \\ Joerg Arndt, Jul 14 2012

(PARI) list(lim)=my(v=List(), p); forstep(s=3, sqrtint(lim\1*8-7), 2, if(isprime(p=(s^2+7)/8), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, May 05 2020

CROSSREFS

Cf. A000040, A000124, A000217, A067186, A110872, A110873, A129545.

Sequence in context: A309471 A073602 A057025 * A361151 A327552 A336342

Adjacent sequences: A055466 A055467 A055468 * A055470 A055471 A055472

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jun 27 2000

STATUS

approved