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.
Since the trailing digit of the base-7 expansion must (like all others) be less than 3, this is a subsequence of A045381.
LINKS
Robert Price, Table of n, a(n) for n = 1..829
EXAMPLE
E.g., 7 = 10_7 and 10_3 = 3 are both prime; 107 = 212_7 and 212_3 = 23 are both prime.
PROG
(PARI) is(p, b=3, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 1e3, is(p, 7, 3)&&print1(vector(#d=digits(p, 3), i, 7^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 7)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 12 2014
STATUS
approved