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%I #6 Sep 18 2022 20:09:32
%S 3,5,17,4517,5477,5867,7457,8537,13877,16067,22697,27917,56477,59357,
%T 90437,97577,101747,118247,122207,124247,135467,139457,140417,153947,
%U 208697,247067,267677,306947,419927,470087,489407,520547,529577,540347
%N Primes p such that 2^j+p^j are primes for j=0,1,2,4.
%e For j=0 1+1=2 is prime; also terms should be lesser-twin-primes
%e because of p^1+2^1=p+2=prime; 3rd and 4th conditions are as
%e follows: prime=p^2+4 and prime=16+p^4.
%t {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}]
%t Select[Prime[Range[45000]],AllTrue[{2+#,4+#^2,16+#^4},PrimeQ]&] (* _Harvey P. Dale_, Sep 18 2022 *)
%Y Cf. A082101, A094473-A094486.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 01 2004
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