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
KEYWORD
nonn,easy
AUTHOR
Parthasarathy Nambi, Sep 26 2005
STATUS
approved