|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|