A094492 Primes p such that 2^j+p^j are primes for j=0,1,4,16.

179, 461, 521, 1877, 4259, 9767, 30389, 33071, 33329, 93701, 120077, 124247, 145547, 163481, 181871, 245627, 344171, 345731, 487427, 492671, 522281, 598187, 700199, 709739, 736061, 769259, 833717, 955709, 966869, 1009649, 1030739

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

Table of n, a(n) for n=1..31.

Example

For j=0 1+1=2 is prime; other conditions are:
because of p^1+2=prime; 3rd and 4th conditions are as
follows: prime=p^4+16 and prime=65536+p^16.

Mathematica

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

Crossrefs

Cf. A082101, A094473-A094491.

Sequence in context: A101795 A142389 A063350 * A162163 A062651 A142611

Adjacent sequences: A094489 A094490 A094491 * A094493 A094494 A094495

Keyword

nonn

Author

Labos Elemer, Jun 01 2004

Status

approved