A235468 Primes whose base-5 representation also is the base-3 representation of a prime.

2, 5, 7, 11, 31, 37, 127, 131, 151, 157, 257, 281, 311, 661, 677, 751, 757, 877, 881, 907, 911, 1277, 1301, 1381, 1511, 1531, 3137, 3187, 3251, 3307, 3407, 3761, 3877, 3911, 3931, 4001, 4007, 4027, 4051, 4057, 4561, 4637, 6257, 6287, 7057, 7151, 7177, 7187, 7507

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

			a(1) = 5 = 10_5 and 10_3 = 3 are both prime.
a(2) = 7 = 12_5 and 12_3 = 5 are both prime.
a(3) = 11 = 21_5 and 21_3 = 7 are both prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..11369
• 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=5)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,1e3,is(p,5,3)&&print1(vector(#d=digits(p,3),i,5^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,3,5)