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A318940 Primes whose binary representation contains a consecutive string of zeros of prime length. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

PROG

(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

CROSSREFS

A subsequence of A319302, which suggested this sequence.

Sequence in context: A288407 A286611 A144213 * A289355 A144214 A191043

Adjacent sequences:  A318937 A318938 A318939 * A318941 A318942 A318943

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Sep 17 2018

EXTENSIONS

More terms from Charlie Neder, Sep 17 2018

STATUS

approved

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Last modified July 26 14:45 EDT 2021. Contains 346294 sequences. (Running on oeis4.)