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

Author

W. Zane Billings, Jul 11 2019

Keywords

• nonn
• easy
• base

Examples

			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.
		

Crossrefs

Cf. A110529, A319302.

Programs

Mathematica

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

Python

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