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A318940 Primes whose binary representation contains a consecutive string of zeros of prime length. 2

%I #25 Nov 26 2018 03:50:16

%S 17,19,37,41,71,73,79,83,89,101,103,113,131,137,139,149,151,157,163,

%T 167,179,193,197,199,211,227,229,233,241,257,263,277,281,283,293,307,

%U 311,313,317,331,337,359,397,401,409,419,421,433,449,457

%N Primes whose binary representation contains a consecutive string of zeros of prime length.

%C Most primes appear to fall into this category. - _Charlie Neder_, Sep 17 2018

%H Charlie Neder, <a href="/A318940/b318940.txt">Table of n, a(n) for n = 1..949</a>

%t 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 *)

%o (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 A subsequence of A319302, which suggested this sequence.

%K nonn,base

%O 1,1

%A _N. J. A. Sloane_, Sep 17 2018

%E More terms from _Charlie Neder_, Sep 17 2018

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)