A094494 - OEIS

%I #12 Apr 18 2024 12:52:19

%S 6203,16067,72367,105653,179743,323903,1005467,1040113,1276243,

%T 1331527,1582447,1838297,1894873,2202433,2314603,2366993,2369033,

%U 2416943,2533627,2698697,2804437,2806613,2823277,2826337,2851867,2888693,3911783,4217617,4432837,4475473

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

%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.

%H Robert Israel, <a href="/A094494/b094494.txt">Table of n, a(n) for n = 1..400</a>

%e Conditions mean 2,p^2+4,16+p^4,256+p^8 are all primes.

%p p:= 2: count:= 0: Res:= NULL:

%p while count < 30 do

%p   p:= nextprime(p);

%p   if isprime(4+p^2) and isprime(16+p^4) and isprime(256+p^8) then

%p     count:= count+1;

%p     Res:= Res, p;

%p   fi

%p od:

%p Res; # _Robert Israel_, Jul 17 2018

%t {ta=Table[0, {100}], u=1}; Do[s0=2;s2=4+Prime[j]^2;s2=16+Prime[j]^4;s8=256+Prime[j]^8 If[PrimeQ[s0]&&PrimeQ[s2]&&PrimeQ[s4]&&PrimeQ[s8], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]

%t Select[Prime[Range[210000]],AllTrue[Table[2^j+#^j,{j,{0,2,4,8}}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 13 2017 *)

%Y Cf. A082101, A094473-A094492.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 01 2004