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A094491 Primes p such that 2^j+p^j are primes for j=0,4,8,128. 3

%I

%S 223,2104547,2403689,4268233,17620457,21848647,23487311,29205821,

%T 42889591,43458859,47899487,48309017,54666847,61227457,73038689,

%U 81742547,83574457,85031153,87285403,95017003,100339517,103136867

%N Primes p such that 2^j+p^j are primes for j=0,4,8,128.

%C Primes of 2^j+p^j form are a generalization of Fermat-primes. 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-A094490.

%e For j=0 1+1=2 is prime; other conditions are: because of p^4+16==prime; 3rd and 4th conditions are as follows: prime=p^8+256 and prime=2^128+p^128.

%t {ta=Table[0, {100}], u=1}; Do[s0=2;s4=16+Prime[j]^4;s8=256+Prime[j]^8;s128=2^128+Prime[j]^128 If[PrimeQ[s0]&&PrimeQ[s4]&&PrimeQ[s8]&&PrimeQ[s128], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]

%Y Cf. A082101, A094473-A094490.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 01 2004

%E a(5)-a(22) from _Donovan Johnson_, Oct 12 2008

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Last modified June 16 09:27 EDT 2021. Contains 345056 sequences. (Running on oeis4.)