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A309092
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Integers whose hexadecimal representation contains a run of zeros of prime length.
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0
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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
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..43.
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range@ 7168, Select[Split@ IntegerDigits[#, 16], #[[1]] == 0 && PrimeQ@ Length@ # &] != {} &] (* Giovanni Resta, Jul 16 2019 *)
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PROG
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(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
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CROSSREFS
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Cf. A110529, A319302.
Sequence in context: A206199 A271811 A255998 * A043336 A256822 A172422
Adjacent sequences: A309089 A309090 A309091 * A309093 A309094 A309095
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KEYWORD
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nonn,easy,base
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AUTHOR
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W. Zane Billings, Jul 11 2019
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STATUS
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approved
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