A094494 Primes p such that 2^j+p^j are primes for j=0,2,4,8.

6203, 16067, 72367, 105653, 179743, 323903, 1005467, 1040113, 1276243, 1331527, 1582447, 1838297, 1894873, 2202433, 2314603, 2366993, 2369033, 2416943, 2533627, 2698697, 2804437, 2806613, 2823277, 2826337, 2851867, 2888693, 3911783, 4217617, 4432837, 4475473

Offset

1,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 1..400

Example

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

Maple

p:= 2: count:= 0: Res:= NULL:
while count < 30 do
  p:= nextprime(p);
  if isprime(4+p^2) and isprime(16+p^4) and isprime(256+p^8) then
    count:= count+1;
    Res:= Res, p;
  fi
od:
Res; # Robert Israel, Jul 17 2018

Mathematica

{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}]
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 *)

Crossrefs

Cf. A082101, A094473-A094492.

Sequence in context: A255791 A186602 A031836 * A235277 A246889 A172629

Adjacent sequences: A094491 A094492 A094493 * A094495 A094496 A094497

Keyword

nonn,changed

Author

Labos Elemer, Jun 01 2004

Status

approved