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 the 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=8, thus a subsequence of A077722.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
73 = 111_8 and 111_2 = 7 are both prime, so 73 is a term.
PROG
(PARI) is(p, b=2, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 8, 2)&&print1(vector(#d=digits(p, 2), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(., 2, 8)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 11 2014
STATUS
approved