A094487 Primes p such that 2^j+p^j are primes for j=0,1,2,4.

3, 5, 17, 4517, 5477, 5867, 7457, 8537, 13877, 16067, 22697, 27917, 56477, 59357, 90437, 97577, 101747, 118247, 122207, 124247, 135467, 139457, 140417, 153947, 208697, 247067, 267677, 306947, 419927, 470087, 489407, 520547, 529577, 540347

Offset: 1

Author

Labos Elemer, Jun 01 2004

Keywords

• nonn

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=16+p^4.
		

Crossrefs

Cf. A082101, A094473-A094486.

Programs

Mathematica

{ta=Table[0, {100}], u=1}; Do[s0=2;s1=Prime[j]+2;s2=4+Prime[j]^2;s4=16+Prime[j]^4; If[PrimeQ[s0]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s4], Print[{j, Prime[j]}];ta[[u]]=Prime[j];u=u+1], {j, 1, 1000000}]
Select[Prime[Range[45000]],AllTrue[{2+#,4+#^2,16+#^4},PrimeQ]&] (* Harvey P. Dale, Sep 18 2022 *)