OFFSET
1,1
COMMENTS
Are all the numbers in this sequence multiples of 3?
Look at the sequence in base 12, with X for ten and E for eleven. Recall that all primes greater than 3 end in 1, 5, 7, E. The sequence [n,(23*n^2+4) mod 12], 0<=n<=11, is [0, 4], [1, 3], [2, 0], [3, 7], [4, 0], [5, 3], [6, 4], [7, 3], [8, 0], [9, 7], [10, 0], [11, 3] so the only possible primes are at 3, 9 mod 12 or only at odd multiples of 3, with the primes being all 7 primes. In base 12 the sequence is [3,157], [9,10E7], [13,2EE7], [49,372E7], [53,449E7], [59,53457], [63,62X57], [69,733E7], [73,848E7], [83,XX557]. - Walter Kehowski, Oct 05 2005
EXAMPLE
If n=99 then (23*n^2) + 4 = 225427 (prime)
MAPLE
select(proc(z) isprime(z[2]) end, [seq([n, 23*n^2 + 4], n=0..9*12)]); (Kehowski)
PROG
(Magma) [n: n in [0..10000] |IsPrime((23*n^2)+4)] - Vincenzo Librandi, Nov 13 2010
(PARI) is(n)=isprime(23*n^2+4) \\ Charles R Greathouse IV, Jun 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Parthasarathy Nambi, Sep 26 2005
STATUS
approved