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

1,1

Links

Table of n, a(n) for n=1..43.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A110529, A319302.

Sequence in context: A206199 A271811 A255998 * A043336 A256822 A172422

Adjacent sequences: A309089 A309090 A309091 * A309093 A309094 A309095

Keyword

nonn,easy,base

Author

W. Zane Billings, Jul 11 2019

Status

approved