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

223, 2104547, 2403689, 4268233, 17620457, 21848647, 23487311, 29205821, 42889591, 43458859, 47899487, 48309017, 54666847, 61227457, 73038689, 81742547, 83574457, 85031153, 87285403, 95017003, 100339517, 103136867

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..22.

Example

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.

Mathematica

{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}]

Crossrefs

Cf. A082101, A094473-A094490.

Sequence in context: A139233 A205265 A153165 * A162604 A296896 A050241

Adjacent sequences: A094488 A094489 A094490 * A094492 A094493 A094494

Keyword

nonn

Author

Labos Elemer, Jun 01 2004

Extensions

a(5)-a(22) from Donovan Johnson, Oct 12 2008

Status

approved