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
Keywords
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..500
Programs
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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 *)