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
Keywords
Examples
(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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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 *) -
PARI
forprime(p=2, 3000, if(isprime(q=(p-1)^4+p^4+(p+1)^4), print1(p, ","))) /* Klaus Brockhaus, Mar 09 2007 */
Extensions
Edited, corrected and extended by Klaus Brockhaus, Mar 09 2007