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.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
19 = 21_9 and 21_6 = 13 are both prime, so 19 is a term.
509 = 625_9 and 625_6 = 17 are both prime, but 625 is not a valid base-6 integer, so 509 is not a term.
MAPLE
R:= 2: x:= 2: count:= 1:
while count < 100 do
x:= nextprime(x);
L:= convert(x, base, 6);
y:= add(9^(i-1)*L[i], i=1..nops(L));
if isprime(y) then count:= count+1; R:= R, y fi
od:
R; # Robert Israel, May 18 2020
PROG
(PARI) is(p, b=6, c=9)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 9, 6)&&print1(vector(#d=digits(p, 6), i, 9^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 6, 9)
CROSSREFS
KEYWORD
AUTHOR
M. F. Hasler, Jan 13 2014
STATUS
approved