A094492 - OEIS

%I #7 Nov 21 2013 12:48:18

%S 179,461,521,1877,4259,9767,30389,33071,33329,93701,120077,124247,

%T 145547,163481,181871,245627,344171,345731,487427,492671,522281,

%U 598187,700199,709739,736061,769259,833717,955709,966869,1009649,1030739

%N Primes p such that 2^j+p^j are primes for j=0,1,4,16.

%C Primes of 2^j+p^j form are a generalization of Fermat-primes. 1^j is replaced by p^j. This is strongly supported by the observation that corresponding j-exponents are apparently powers of 2 like for the 5 known Fermat primes. See A094473-A094491.

%e For j=0 1+1=2 is prime; other conditions are:

%e because of p^1+2=prime; 3rd and 4th conditions are as

%e follows: prime=p^4+16 and prime=65536+p^16.

%t {ta=Table[0, {100}], u=1}; Do[s0=2;s1=2+Prime[j]^1;s8=16+Prime[j]^4;s16=65536+Prime[j]^16 If[PrimeQ[s0]&&PrimeQ[s4]&&PrimeQ[s8]&&PrimeQ[s128], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]

%t With[{j={0,1,4,16}},Select[Prime[Range[81000]],And@@PrimeQ[2^j+#^j]&]] (* _Harvey P. Dale_, Oct 17 2011 *)

%Y Cf. A082101, A094473-A094491.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 01 2004