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A126112
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Prime numbers p such that p^4 + (p-1)^4 + (p+1)^4 is a prime number.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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EXAMPLE
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(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.
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MATHEMATICA
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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 *)
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PROG
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(PARI) {forprime(p=2, 3000, if(isprime(q=(p-1)^4+p^4+(p+1)^4), print1(p, ", ")))] /* Klaus Brockhaus, Mar 09 2007 */
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CROSSREFS
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Cf. A126657, A126769, A126113.
Sequence in context: A035095 A066674 A125878 * A194373 A156210 A264803
Adjacent sequences: A126109 A126110 A126111 * A126113 A126114 A126115
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KEYWORD
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nonn
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AUTHOR
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Tomas Xordan, Mar 05 2007
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EXTENSIONS
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Edited, corrected and extended by Klaus Brockhaus, Mar 09 2007
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STATUS
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approved
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