A126112 Prime numbers p such that p^4 + (p-1)^4 + (p+1)^4 is a prime number.

3, 7, 11, 29, 31, 53, 59, 83, 109, 127, 283, 349, 461, 521, 599, 643, 683, 787, 809, 829, 907, 911, 937, 983, 1093, 1117, 1201, 1289, 1301, 1487, 1523, 1613, 1721, 1877, 2017, 2153, 2267, 2281, 2423, 2521, 2579, 2657, 2677, 2699, 2731, 2741, 2797, 2887, 2969

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

(3-1)^4 + 3^4 + (3+1)^4 = 2^4 + 3^4 + 4^4 = 16 + 81 + 256 = 353 is prime, hence 3 is a term.
(11-1)^4 + 11^4 + (11+1)^4 = 10^4 + 11^4 + 12^4 = 10000 + 14641 + 20736 = 45377 is prime, hence 11 is a term.

Mathematica

f[n_]:=PrimeQ[(n-1)^4+n^4+(n+1)^4]; lst={}; Do[p=Prime[n]; If[f[p], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)
Select[Prime[Range[500]], PrimeQ[Total[(#+{-1, 0, 1})^4]]&] (* Harvey P. Dale, Dec 07 2012 *)

Prog

(PARI) forprime(p=2, 3000, if(isprime(q=(p-1)^4+p^4+(p+1)^4), print1(p, ", "))) /* Klaus Brockhaus, Mar 09 2007 */

Crossrefs

Cf. A126657, A126769, A126113.

Sequence in context: A035095 A066674 A125878 * A194373 A156210 A343718

Adjacent sequences: A126109 A126110 A126111 * A126113 A126114 A126115

Keyword

nonn

Author

Tomas Xordan, Mar 05 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Mar 09 2007

Status

approved