A049001 a(n) = prime(n)^2 - 2.

2, 7, 23, 47, 119, 167, 287, 359, 527, 839, 959, 1367, 1679, 1847, 2207, 2807, 3479, 3719, 4487, 5039, 5327, 6239, 6887, 7919, 9407, 10199, 10607, 11447, 11879, 12767, 16127, 17159, 18767, 19319, 22199, 22799, 24647, 26567, 27887

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Smallest numbers k such that k*prime(n)^2 + 1 is a square. - Bruno Berselli, Apr 19 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Barry Brent, On the constant terms of certain meromorphic modular forms for Hecke groups, arXiv:2212.12515 [math.NT], 2022.
• Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.

Crossrefs

Cf. A001248, A049002, A065481.

Cf. A084920, A166010, A182200; A182174.

Programs

Haskell

a049001 = subtract 2 . a001248  -- Reinhard Zumkeller, Jul 30 2015

Maple

A049001:=n->ithprime(n)^2-2; seq(A049001(k), k=1..50); # Wesley Ivan Hurt, Oct 11 2013

Mathematica

Table[Prime[n]^2-2, {n, 50}] (* Wesley Ivan Hurt, Oct 11 2013 *)

PARI

a(n) = prime(n)^2 - 2; \\ Amiram Eldar, Nov 07 2022

Formula

a(n) = A001248(n) - 2.

a(n) = A182200(n) + 1. - Wesley Ivan Hurt, Oct 11 2013

Product_{n>=1} (1 - 1/a(n)) = A065481. - Amiram Eldar, Nov 07 2022