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A309092 Integers whose hexadecimal representation contains a run of zeros of prime length. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 12:10 EDT 2021. Contains 348088 sequences. (Running on oeis4.)