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
Both 13 = 21_6 and 21_5 = 11 are prime.
MAPLE
P:= {seq(ithprime(i), i=1..10000)}:
f:= proc(p) local i, L;
L:= convert(p, base, 5);
add(L[i]*6^(i-1), i=1..nops(L))
end proc:
sort(convert(map(f, P) intersect P, list)); # Robert Israel, Jun 18 2019
MATHEMATICA
b65pQ[n_]:=Module[{idn6=IntegerDigits[n, 6]}, Max[idn6]<5&&PrimeQ[ FromDigits[ idn6, 5]]]; Select[Prime[Range[600]], b65pQ] (* Harvey P. Dale, Oct 13 2020 *)
PROG
(PARI) is(p, b=5, c=6)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 6, 5)&&print1(vector(#d=digits(p, 5), i, 6^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 4, 6)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Jan 13 2014
STATUS
approved