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 A318940 #27 Jul 30 2025 17:05:30
%S A318940 17,19,37,41,71,73,79,83,89,101,103,113,131,137,139,149,151,157,163,
%T A318940 167,179,193,197,199,211,227,229,233,241,257,263,277,281,283,293,307,
%U A318940 311,313,317,331,337,359,397,401,409,419,421,433,449,457
%N A318940 Primes whose binary representation contains a consecutive string of zeros of prime length.
%C A318940 Most primes appear to fall into this category. - _Charlie Neder_, Sep 17 2018
%H A318940 Charlie Neder, <a href="/A318940/b318940.txt">Table of n, a(n) for n = 1..949</a>
%t A318940 Prime@ Position[Array[If[Length@ # == 0, {0}, Length /@ #] &@ DeleteCases[Split@ IntegerDigits[Prime@ #, 2], _?(First@ # == 1 &)] &, 100], _?(AnyTrue[#, PrimeQ] &), {1}, Heads -> False][[All, 1]] (* _Michael De Vlieger_, Nov 25 2018 *)
%t A318940 brpQ[p_]:=AnyTrue[Length/@Select[Split[IntegerDigits[p,2]],#[[1]]==0&],PrimeQ]; Select[Prime[Range[100]],brpQ] (* _Harvey P. Dale_, Jul 30 2025 *)
%o A318940 (PARI) ok(n)={if(isprime(n), while(n, my(t=valuation(n,2)); if(isprime(t), return(1)); n >>= t + 1)); 0} \\ _Andrew Howroyd_, Nov 09 2018
%Y A318940 A subsequence of A319302, which suggested this sequence.
%K A318940 nonn,base
%O A318940 1,1
%A A318940 _N. J. A. Sloane_, Sep 17 2018
%E A318940 More terms from _Charlie Neder_, Sep 17 2018