A110959 Numbers n such that 23*n^2 + 1 is prime.

6, 12, 24, 66, 72, 84, 90, 96, 132, 144, 150, 162, 174, 180, 186, 204, 210, 216, 222, 234, 252, 264, 288, 342, 360, 372, 384, 390, 396, 408, 438, 444, 456, 474, 516, 522, 534, 546, 576, 606, 612, 630, 648, 702, 720, 750, 762, 768, 780, 810, 828, 834, 840, 882

Offset

1,1

Comments

Are all the terms in this sequence divisible by 6?

Let's look at the sequence in base 12 with X for ten and E for eleven. Recall that all primes greater than three end in a 1, 5, 7, or E. The sequence [n,(23*n^2+1)mod 12], 0<=n<=11, is [0, 1], [1, 0], [2, 9], [3, 4], [4, 9], [5, 0], [6, 1], [7, 0], [8, 9], [9, 4], [10, 9], [11, 0]. Thus the only possible primes are in 0 or 6 mod 12, that is, all multiples of 6 and all such primes end in 1. The sequence in base 12 is [6,591],[10,1E01], [20,7801], [56,49E91], [60,59001], [70,79E01], [76,8E991], [80,X2801]. - Walter Kehowski, Oct 05 2005

Links

Table of n, a(n) for n=1..54.

Example

If n=144 then (23*n^2) + 1 = 476929 (prime).

Maple

select(proc(z) isprime(z[2]) end, [seq([n, 23*n^2 + 1], n=0..9*12)]); (Kehowski)

Mathematica

Select[Range[900], PrimeQ[23*#^2+1]&] (* James C. McMahon, Apr 26 2024 *)

Prog

A110959 (Magma) [n: n in [0..10000] |IsPrime((23*n^2)+1)] - Vincenzo Librandi, Nov 13 2010
(PARI) is(n)=isprime(23*n^2+1) \\ Charles R Greathouse IV, Jun 12 2017

Crossrefs

Sequence in context: A089529 A300915 A001766 * A303398 A244743 A202805

Adjacent sequences: A110956 A110957 A110958 * A110960 A110961 A110962

Keyword

nonn,easy

Author

Parthasarathy Nambi, Sep 26 2005

Status

approved