A235469 Primes whose base-6 representation also is the base-3 representation of a prime.

2, 13, 43, 73, 223, 1777, 2593, 2887, 3037, 3067, 3109, 7993, 9157, 9337, 10597, 17077, 17107, 17137, 17317, 17359, 18229, 18661, 46663, 48247, 49297, 49537, 54517, 54727, 54877, 54907, 54949, 55987, 56197, 56209, 56239, 57097, 63589, 63727, 64879, 65089, 65101, 95089, 95917, 96157

Offset: 1

Author

M. F. Hasler, Jan 12 2014

Keywords

• nonn
• base

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.

Examples

			E.g., 13 = 21_6 and 21_3 = 7 are both prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..1959
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Programs

PARI

is(p,b=3,c=6)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,1e3,is(p,6,3)&&print1(vector(#d=digits(p,3),i,6^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,3,6)