A235627 Primes whose base-7 representation also is the base-5 representation of a prime.

2, 3, 7, 17, 23, 31, 53, 71, 73, 79, 101, 109, 113, 127, 151, 157, 197, 199, 359, 401, 409, 449, 463, 521, 541, 557, 743, 863, 1033, 1039, 1103, 1151, 1193, 1229, 1451, 1487, 1499, 1543, 2423, 2521, 2549, 2621, 2753, 2857, 2909, 2957, 3089, 3257, 3313, 3511, 3529, 3593

Offset

1,1

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.

Links

Robert Price, Table of n, a(n) for n = 1..13736

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

Example

Both 17 = 23_7 and 23_5 = 13 are prime.

Prog

(PARI) is(p, b=5, c=7)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 7, 5)&&print1(vector(#d=digits(p, 5), i, 7^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 5, 7)

Crossrefs

Cf. A235635, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Sequence in context: A045332 A045333 A040141 * A019335 A113425 A289379

Adjacent sequences: A235624 A235625 A235626 * A235628 A235629 A235630

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved