A235464 Primes whose base-7 representation also is the base-2 representation of a prime.

7, 2801, 17207, 19559, 134513, 134807, 840743, 842759, 842801, 941249, 943601, 958007, 958049, 958343, 5899657, 6591089, 6607903, 6706393, 6722857, 41196751, 41311663, 41314057, 46137673, 46137967, 46253257, 46942351, 46944409, 47059657

Offset: 1

Author

M. F. Hasler, Jan 11 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.

When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=7, thus a subsequence of A077721.

Examples

			7 = 10_7 and 10_2 = 2 are both prime, so 7 is a term.
2801 = 11111_7 and 11111_2 = 31 are both prime, so 2801 is a term.
		

Links

• M. F. Hasler, Primes whose base c expansion is also the base b expansion of a prime

Crossrefs

Cf. A235477, 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=2,c=7)=vecmax(d=digits(p,c))
				

PARI

forprime(p=1,1e3,is(p,7,2)&&print1(vector(#d=digits(p,2),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(.,2,7)