A225787 Least prime number p such that p*triangular(n) is a triangular number, or 0 if no such p exists.

2, 3, 2, 11, 19, 3, 5, 0, 71, 23, 109, 131, 17, 181, 2, 239, 271, 307, 0, 379, 3, 13, 127, 61, 67, 163, 701, 47, 811, 97, 37, 991, 0, 31, 0, 79, 83, 0, 41, 7, 0, 191, 37, 0, 5, 83, 541, 251, 2351, 613, 71, 0, 0, 2861, 743, 3079, 3191, 367, 0, 3539, 229, 0, 977, 0, 4159

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) <= n^2 + n + 2. For n>0, a(n) <= n^2 + n + 1.

Example

Least prime p such that triangular(3)*p is a triangular number is p=11, so a(3) = 11.

Maple

f:= proc(n) local m, y, S;
  m:= 4*n*(n+1);
  S:= map(t -> rhs(op(t)), [msolve(y^2-1, m)]);
  S:= select(isprime, map(t -> (t^2-1)/m, S));
  if S = [] then 0 else min(S) fi
end proc:
f(0):= 2:
map(f, [$0..100]); # Robert Israel, Nov 04 2025

Crossrefs

Cf. A000217, A068084, A225502. Cf. A053141 (n such that a(n) = 2).

Sequence in context: A224418 A220947 A224417 * A012960 A013117 A120864

Adjacent sequences: A225784 A225785 A225786 * A225788 A225789 A225790

Keyword

nonn

Author

Alex Ratushnyak, May 16 2013

Status

approved