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%I #9 Jun 01 2017 10:39:46
%S 1,1,8860,1,6822,601,7912,65093,81430,11383,5066,54667,9618,28149,236,
%T 85,140,953,1260,119,5206,19555,788,1955,246,7701,170,255,58514,91511,
%U 30750,6237,45508,1725,272,16985,5712,225,81520,1587,54560,4607,7710
%N Smallest k such that n^8+k^8, n^4+k^4, n^2+k^2, n+k are simultaneously prime.
%t Do[k = 1; While[ !PrimeQ[n + k] || !PrimeQ[n^2 + k^2] || !PrimeQ[n^4 + k^4] || !PrimeQ[n^8 + k^8], k++ ]; Print[k], {n, 1, 45}]
%t sk[n_]:=Module[{k=1},While[!AllTrue[{n^8+k^8,n^4+k^4,n^2+k^2,n+k}, PrimeQ], k++]; k]; Array[sk,45] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 01 2017 *)
%o (PARI) for(n=1,7,s=1; while(isprime(s^2+n^2)*isprime(s+n)*isprime(s^4+n^4)*isprime(s^8+n^8)==0,s++); print1(s,","))
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, May 30 2002
%E Edited by _Robert G. Wilson v_, Jun 07 2002
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