

A055469


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


19



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
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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 *)


PROG

(PARI) forprime(p=2, 10^5, if ( issquare(8*p7), print1(p, ", "))) \\ Joerg Arndt, Jul 14 2012
(PARI) list(lim)=my(v=List(), p); forstep(s=3, sqrtint(lim\1*87), 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 * A327552 A336342 A284354
Adjacent sequences: A055466 A055467 A055468 * A055470 A055471 A055472


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Jun 27 2000


STATUS

approved



