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

Offset: 1

Author

Henry Bottomley, Jun 27 2000

Keywords

• nonn
• easy

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

Crossrefs

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

Programs

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 *)

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

Formula

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