A110974 Numbers n such that 23*n^2 - 1 is prime.

4, 6, 8, 14, 18, 20, 22, 38, 52, 60, 62, 64, 84, 90, 92, 94, 108, 126, 130, 134, 140, 146, 148, 150, 168, 172, 176, 178, 192, 202, 220, 224, 242, 286, 290, 300, 304, 308, 316, 326, 328, 344, 346, 350, 354, 360, 378, 396, 398, 400

Offset

1,1

Comments

Let's look at the sequence in base 12 with X for ten and E for eleven. Recall that in base 12 all primes greater than 3 end in either 1, 5, 7, or E. The sequence [n,(23*n^2-1) mod 12], 0<=n<=11, is [0, E], [1, 10], [2, 7], [3, 2], [4, 7], [5, 10], [6, E], [7, 10], [8, 7], [9, 2], [10, 7], [11, 10] so the only possibilities for primes are at the even integers with 7 and E primes, with 7 primes at 2, 4, 8, X mod 12 and E primes at 0, 6 mod 12. The sequence in base 12 is [4,267], [6,58E], [8,X27], [12,2737], [16,438E], [18,53X7], [1X,6537], [32,17277], [44,2EEX7], [50,3EXEE], [52,431E7], [54,46627], [70,79XEE], [76,8E98E], [78, 947X7], [7X,99737], [90,10E2EE]. - Walter Kehowski, Oct 05 2005

Links

Table of n, a(n) for n=1..50.

Example

If n=94 then 23*n^2 - 1 = 203227 (prime).

Maple

select(proc(z) isprime(z[2]) end, [seq([n, 23*n^2 - 1], n=0..9*12)]); # Walter Kehowski

Mathematica

Select[Range[400], PrimeQ[(23#^2 - 1)] &] (* Stefan Steinerberger, Feb 28 2006 *)

Prog

(Magma) [ n: n in [0..1500] | IsPrime( 23*n^2 - 1) ] // Vincenzo Librandi, Jan 31 2011
(PARI) isok(n) = isprime(23*n^2 - 1); \\ Michel Marcus, Sep 16 2015

Crossrefs

Sequence in context: A050902 A374190 A320125 * A173180 A200077 A256137

Adjacent sequences: A110971 A110972 A110973 * A110975 A110976 A110977

Keyword

nonn

Author

Parthasarathy Nambi, Sep 27 2005

Extensions

More terms from Stefan Steinerberger, Feb 28 2006

Status

approved