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%I #20 Sep 08 2022 08:45:20
%S 2,8,10,14,16,20,28,32,34,40,44,46,52,76,80,92,98,106,122,124,128,136,
%T 140,142,146,154,158,166,172,182,184,188,190,194,196,208,218,232,244,
%U 262,268,272,274,278,280,284,296,310,320,326,332,346,356,358,364,374
%N Numbers n such that 23*n^2 + 9 is prime.
%C 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
%H Robert Israel, <a href="/A110961/b110961.txt">Table of n, a(n) for n = 1..10000</a>
%e If n=98 then (23*n^2) + 9 = 220901 (prime).
%p select(proc(z) isprime(z[2]) end, [seq([n,23*n^2 + 9],n=0..9*12)]); # _Walter Kehowski_, Oct 05 2005
%o (Magma) [n: n in [2..100000] |IsPrime((23*n^2)+9)] // _Vincenzo Librandi_, Nov 13 2010
%o (PARI) is(n)=isprime(23*n^2+9) \\ _Charles R Greathouse IV_, Jun 12 2017
%K nonn,easy
%O 1,1
%A _Parthasarathy Nambi_, Sep 26 2005