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

17, 19, 37, 41, 71, 73, 79, 83, 89, 101, 103, 113, 131, 137, 139, 149, 151, 157, 163, 167, 179, 193, 197, 199, 211, 227, 229, 233, 241, 257, 263, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 359, 397, 401, 409, 419, 421, 433, 449, 457

Offset: 1

Author

N. J. A. Sloane, Sep 17 2018

Keywords

• nonn
• base

Comments

Most primes appear to fall into this category. - Charlie Neder, Sep 17 2018

Links

• Charlie Neder, Table of n, a(n) for n = 1..949

Crossrefs

A subsequence of A319302, which suggested this sequence.

Programs

Mathematica

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 *)
brpQ[p_]:=AnyTrue[Length/@Select[Split[IntegerDigits[p,2]],#[[1]]==0&],PrimeQ]; Select[Prime[Range[100]],brpQ] (* Harvey P. Dale, Jul 30 2025 *)

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

Extensions

More terms from Charlie Neder, Sep 17 2018