A236431 Numbers n such that both prime(n)+n and prime(n)-n give a triangular number.

1, 513, 213796

Offset

1,2

Comments

Intersection of A115882 and A115883.

The corresponding primes are 2, 3673, 2955107.

No more terms up to 10^12. - Giovanni Resta, Jan 26 2014

Links

Table of n, a(n) for n=1..3.

Example

prime(1) is 2, and both 2+1=3 and 2-1=1 are triangular.

Mathematica

Select[Range[214000], AllTrue[{Sqrt[8(Prime[#]-#)+1], Sqrt[8(Prime[#]+#)+ 1]}, OddQ]&] (* Harvey P. Dale, Jul 22 2022 *)

Prog

(PARI) lista(nn) = {p = primes(nn); for (n=1, #p, pn = p[n]; if (ispolygonal(pn - n, 3) && ispolygonal(pn + n, 3), print1(n, ", ")); ); }

Crossrefs

Cf. A115882, A115883.

Sequence in context: A168118 A086030 A094647 * A118709 A296145 A283369

Adjacent sequences: A236428 A236429 A236430 * A236432 A236433 A236434

Keyword

nonn,bref,more

Author

Michel Marcus, Jan 25 2014

Status

approved