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
Alois P. Heinz, Table of n, a(n) for n = 1..10000
EXAMPLE
E.g., 17 = 21_8 and 21_3 = 7 are both prime.
MATHEMATICA
b8b3pQ[n_]:=Module[{id8=IntegerDigits[n, 8]}, Max[id8]<3&&PrimeQ[ FromDigits[ id8, 3]]]; Select[Prime[Range[160000]], b8b3pQ] (* Harvey P. Dale, Mar 16 2019 *)
PROG
(PARI) is(p, b=3, 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, 3)&&print1(vector(#d=digits(p, 3), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 3, 8)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 12 2014
STATUS
approved