OFFSET
1,1
COMMENTS
This sequence is part of the two-dimensional array of sequences based on this same idea for any two different bases b, c > 1. Sequence A235265 and A235266 are the most elementary ones in this list. Sequences A089971, A089981 and A090707 through A090721, and sequences A065720 - A065727, follow the same idea with one base equal to 10.
For further motivation and cross-references, see sequence A235265 which is he main entry for this whole family of sequences.
When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=5, thus a subsequence of A077719.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
5 = 10_5 and 10_2 = 2 are both prime, so 5 is a term.
31 = 111_5 and 111_2 = 7 are both prime, so 31 is a term.
MATHEMATICA
b5b2Q[n_]:=Module[{idn5=IntegerDigits[n, 5]}, Max[idn5]<2 && PrimeQ[ FromDigits[ idn5, 2]]]; Select[Prime[Range[180000]], b5b2Q] (* Harvey P. Dale, Sep 21 2018 *)
PROG
(PARI) is(p, b=2, c=5)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(Python)
from itertools import islice
from sympy import isprime, nextprime
def A235462_gen(): # generator of terms
p = 1
while (p:=nextprime(p)):
if isprime(m:=int(bin(p)[2:], 5)):
yield m
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 11 2014
STATUS
approved