This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370523 #29 Mar 19 2024 12:41:39
%S A370523 4,7,9,15,21,33,45,63,75,105,153,183,195,243,273,285,435,525,573,603,
%T A370523 813,825,1065,1233,1305,1623,2145,2595,2715,2805,3375,3465,3933,4023,
%U A370523 4245,4275,4653,4803,4935,5655,6303,6705,7563,8865,10095,10503,10863,12165,12243,12825,13713,13725,14013
%N A370523 Numbers k > 2 such that all positive values of k - 2^(2^m) are prime, with integer m >= 0.
%C A370523 If k > 4 is a term of this sequence, then (k-2, k-4) is a twin prime pair.
%C A370523 So all terms k > 7 are divisible by 3, and k = 7 is the only prime here.
%C A370523 It seems that there are infinitely many such numbers.
%C A370523 Note that A039669 is finite and probably complete.
%e A370523 The number 15 is a term, since 15-2^(2^0) and 15-2^(2^1) are primes 13 and 11.
%t A370523 q[k_] := Module[{m = 0}, While[2^(2^m) < k && PrimeQ[k - 2^(2^m)], m++]; 2^(2^m) >= k]; Select[Range[4, 15000], q] (* _Amiram Eldar_, Feb 22 2024 *)
%Y A370523 Cf. A039669, A129613.
%K A370523 nonn
%O A370523 1,1
%A A370523 _Thomas Ordowski_, Feb 22 2024
%E A370523 More terms from _Amiram Eldar_, Feb 22 2024