A110960 Numbers n such that 23*n^2 + 4 is prime.

3, 9, 15, 57, 63, 69, 75, 81, 87, 99, 117, 129, 141, 147, 153, 177, 207, 219, 273, 285, 291, 309, 327, 351, 363, 375, 405, 411, 453, 465, 477, 483, 489, 537, 543, 561, 615, 621, 627, 639, 663, 699, 753, 759, 789, 795, 801, 831, 837, 867, 873, 915, 933, 939

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

Links

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

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

Sequence in context: A120403 A247967 A062804 * A192165 A050869 A323679

Adjacent sequences: A110957 A110958 A110959 * A110961 A110962 A110963

Keyword

nonn,easy,changed

Author

Parthasarathy Nambi, Sep 26 2005

Status

approved