A285791 Primes equal to a heptagonal number plus 1.

2, 19, 113, 149, 541, 617, 971, 1289, 1783, 2357, 3011, 3187, 5689, 6427, 7481, 7757, 9829, 12497, 12853, 14327, 15881, 17099, 18793, 21023, 24851, 28463, 30637, 31193, 45361, 50909, 54539, 60607, 63761, 66179, 69473, 70309, 83449, 88079, 90917, 91873, 94771

Offset: 1

Author

Colin Barker, Apr 26 2017

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000566, A002496, A055469, A285789, A285790, A285792.

Programs

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
maxk=300; L=List(); for(k=1, maxk, if(isprime(p=pg(7, k) + 1), listput(L, p))); Vec(L)

Python

from sympy import isprime
def heptagonal(n): return n*(5*n-3)//2
def aupto(limit):
  alst, n, hn = [], 1, heptagonal(1)
  while hn < limit:
    if isprime(hn+1): alst.append(hn+1)
    n, hn = n+1, heptagonal(n+1)
  return alst
print(aupto(94771)) # Michael S. Branicky, Feb 19 2021