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 A055469 Primes of the form k(k+1)/2+1 (i.e., central polygonal numbers, or one more than triangular numbers). 20
 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

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Last modified June 17 13:47 EDT 2024. Contains 373445 sequences. (Running on oeis4.)