A094488 Primes p such that 2^j+p^j are primes for j=0,1,2,8.

137, 2087, 2687, 16067, 24107, 29207, 154787, 155537, 223007, 331907, 427877, 662897, 708137, 769997, 802127, 849047, 869597, 891887, 1031117, 1068497, 1261487, 1336337, 1712567, 1794677, 1807997, 1838297, 1990577, 2189987

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

For j=0 1+1=2 is prime; also terms should be lesser-twin-primes
because of p^1+2^1=p+2=prime; 3rd and 4th conditions are as
follows: prime=p^2+4 and prime=256+p^8.

Mathematica

{ta=Table[0, {100}], u=1}; Do[s0=2; s1=Prime[j]+2; s2=4+Prime[j]^2; s8=256+Prime[j]^8; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s8], Print[{j, Prime[j]}]; ta[[u]]=Prime[j]; u=u+1], {j, 1, 1000000}]
Select[Prime[Range[200000]], AllTrue[{#+2, #^2+4, #^8+256}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 03 2018 *)

Crossrefs

Cf. A082101, A094473-A094487.

Sequence in context: A136080 A215864 A190307 * A221346 A138348 A278175

Adjacent sequences: A094485 A094486 A094487 * A094489 A094490 A094491

Keyword

nonn

Author

Labos Elemer, Jun 01 2004

Status

approved