A235638 Primes whose base-8 representation also is the base-6 representation of a prime.

2, 3, 5, 13, 17, 29, 37, 41, 73, 97, 109, 137, 149, 173, 193, 197, 229, 233, 281, 293, 337, 521, 541, 557, 601, 613, 617, 673, 677, 733, 797, 877, 1033, 1061, 1069, 1117, 1129, 1217, 1237, 1301, 1321, 1381, 1549, 1553, 1609, 1621, 1693, 1733, 1889, 1901, 2069, 2137, 2221, 2273, 2309

Offset: 1

Author

M. F. Hasler, Jan 13 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.

Examples

			E.g., 13 = 15_8 and 15_6 = 11 are both prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..11493
• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235631, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

PARI

is(p,b=6,c=8)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,3e3,is(p,8,6)&&print1(vector(#d=digits(p,6),i,8^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,6,8)