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A090873 a(n) is the smallest number m such that n^2^k + m^2^k is prime for k=0,1,2,3 and 4.

%I A090873 #13 Oct 27 2024 03:21:52
%S A090873 1,1,218368,9324385,6628674,601,365082,532253,449140,4193407,175746,
%T A090873 2857547,2752708,6315245,80612,3354745,10892,953,6577504,157437,
%U A090873 2247676,11357637,7650,272935,318784,8034141,1158380,22315,610550,340357
%N A090873 a(n) is the smallest number m such that n^2^k + m^2^k is prime for k=0,1,2,3 and 4.
%H A090873 Kellen Shenton, <a href="/A090873/b090873.txt">Table of n, a(n) for n = 1..10000</a>
%F A090873 a[n_] := (For[m=1, !(PrimeQ[m+n]&&PrimeQ[m^2+n^2]&&PrimeQ[m^4+n^4]&& PrimeQ[m^8+n^8]&&PrimeQ[m^16+n^16]), m++ ];m)
%e A090873 a(2)=1 because 2^2^k + 1 is prime for k= 0,1,2,3 and 4.
%t A090873 a[n_] := (For[m=1, !(PrimeQ[m+n]&&PrimeQ[m^2+n^2]&&PrimeQ[m^4+n^4]&& PrimeQ[m^8+n^8]&&PrimeQ[m^16+n^16]), m++ ];m);Do[Print[a[n]], {n, 50}]
%Y A090873 Cf. A090872, A019434, A000215.
%K A090873 nonn
%O A090873 1,3
%A A090873 _Farideh Firoozbakht_, Feb 06 2004