

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
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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



