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A319302 Integers whose binary representation contains a consecutive string of zeros of prime length. 3
4, 8, 9, 12, 17, 18, 19, 20, 24, 25, 28, 32, 34, 35, 36, 37, 38, 39, 40, 41, 44, 49, 50, 51, 52, 56, 57, 60, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 88, 89, 92, 96, 98, 99, 100, 101, 102, 103, 104, 105, 108, 113, 114, 115, 116, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

EXAMPLE

81 = (1010001)_2 is a term because it contains a run of zeros of length 3, and 3 is a prime. 16 = (10000)_2 is not a term because it contains only a run of 4 zeros and 4 is not a prime.

MATHEMATICA

Select[Range[120], AnyTrue[ Differences@ Flatten@ Position[ IntegerDigits[ 2*# + 1, 2], 1] - 1, PrimeQ] &] (* Giovanni Resta, Sep 17 2018 *)

PROG

(PARI) is(n) = my(b=binary(n), i=0); for(k=1, #b, if(b[k]==0, i++); if(b[k]==1 || k==#b, if(ispseudoprime(i), return(1), i=0))); 0 \\ Felix Fröhlich, Sep 17 2018

(Python)

from re import split

from sympy import isprime

A319302_list, n = [], 1

while len(A319302_list) < 10000:

for d in split('1+', bin(n)[2:]):

if isprime(len(d)):

A319302_list.append(n)

break

n += 1 # Chai Wah Wu, Oct 02 2018

CROSSREFS

Cf. A004753, A318940.

Sequence in context: A244032 A321454 A353834 * A119025 A167903 A074661

Adjacent sequences: A319299 A319300 A319301 * A319303 A319304 A319305

KEYWORD

nonn,base,easy

AUTHOR

W. Zane Billings, Sep 16 2018

EXTENSIONS

More terms from Giovanni Resta, Sep 17 2018

STATUS

approved

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Last modified December 9 19:36 EST 2022. Contains 358703 sequences. (Running on oeis4.)