A110961 Numbers n such that 23*n^2 + 9 is prime.

2, 8, 10, 14, 16, 20, 28, 32, 34, 40, 44, 46, 52, 76, 80, 92, 98, 106, 122, 124, 128, 136, 140, 142, 146, 154, 158, 166, 172, 182, 184, 188, 190, 194, 196, 208, 218, 232, 244, 262, 268, 272, 274, 278, 280, 284, 296, 310, 320, 326, 332, 346, 356, 358, 364, 374

Offset

1,1

Comments

Look at the sequence in base 12, with X for 10 and E for eleven. Recall that primes greater than 3 end in 1, 5, 7, or 11. The sequence [n, (23*n^2 +9) mod 12] is [0, 9], [1, 8], [2, 5], [3, 0], [4, 5], [5, 8], [6, 9], [7, 8], [8, 5], [9, 0], [10, 5], [11, 8]. Primes can occur only if n mod 12 is 2, 4, 8, 10, or even numbers not divisible by 3 and the only primes that can occur are 5 primes. In base 12 the sequence is [2,85], [8,X35], [X,1405], [12,2745], [14,34E5],[18,53E5], [24,X535], [28,11775], [2X,13485], [34,19375], [38,21935], [3X,24205],[44,2EEE5], [64,64X75], [68,71235], [78,947E5], [82,X7X05], [8X,105685]. - Walter Kehowski, Oct 05 2005

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

If n=98 then (23*n^2) + 9 = 220901 (prime).

Maple

select(proc(z) isprime(z[2]) end, [seq([n, 23*n^2 + 9], n=0..9*12)]); # Walter Kehowski, Oct 05 2005

Prog

(Magma) [n: n in [2..100000] |IsPrime((23*n^2)+9)] // Vincenzo Librandi, Nov 13 2010
(PARI) is(n)=isprime(23*n^2+9) \\ Charles R Greathouse IV, Jun 12 2017

Crossrefs

Sequence in context: A303358 A176464 A102278 * A213535 A161349 A336176

Adjacent sequences: A110958 A110959 A110960 * A110962 A110963 A110964

Keyword

nonn,easy

Author

Parthasarathy Nambi, Sep 26 2005

Status

approved