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User: W. Zane Billings

W. Zane Billings has authored 2 sequences.

A309092 Integers whose hexadecimal representation contains a run of zeros of prime length.

256, 512, 768, 1024, 1280, 1536, 1792, 2048, 2304, 2560, 2816, 3072, 3328, 3584, 3840, 4096, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4352, 4608, 4864, 5120, 5376, 5632, 5888, 6144, 6400, 6656, 6912, 7168

Offset: 1

W. Zane Billings, Jul 11 2019

			256 = 100_(16) is a term because 100 has a run of two zeros, and two is prime. 258 = 102_(16) is not a term, because its only run of zeros is of length 1, which is not prime.

Cf. A110529, A319302.

Select[Range@ 7168, Select[Split@ IntegerDigits[#, 16], #[[1]] == 0 && PrimeQ@ Length@ # &] != {} &] (* Giovanni Resta, Jul 16 2019 *)

from re import split
from sympy import isprime
seq_list, n = [],1
while len(seq_list) < 10000:
    for d in split('[1-9]+|[a-f]+', format(n,'x')):
        if isprime(len(d)):
            seq_list.append(n)
    n += 1

A319302 Integers whose binary representation contains a consecutive string of zeros of prime length.

Original entry on oeis.org

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

Offset: 1

W. Zane Billings, Sep 16 2018

			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.

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

Cf. A004753, A318940.

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

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

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

More terms from Giovanni Resta, Sep 17 2018

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User: W. Zane Billings

A309092 Integers whose hexadecimal representation contains a run of zeros of prime length.

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