A235470 Primes whose base-7 representation also is the base-3 representation of a prime.

2, 7, 107, 401, 443, 457, 701, 743, 751, 2417, 2753, 2843, 2851, 3089, 5147, 5153, 5503, 16823, 16921, 17207, 17257, 17551, 19553, 19993, 21617, 21673, 22003, 22303, 33623, 33679, 33721, 34301, 36017, 36373, 36457, 38873, 118057, 118343, 134507, 134857, 135151, 137251, 137593, 140057

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.

Since the trailing digit of the base-7 expansion must (like all others) be less than 3, this is a subsequence of A045381.

Examples

			E.g., 7 = 10_7 and 10_3 = 3 are both prime; 107 = 212_7 and 212_3 = 23 are both prime.
		

Links

• Robert Price, Table of n, a(n) for n = 1..829
• 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=7)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,1e3,is(p,7,3)&&print1(vector(#d=digits(p,3),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,3,7)