A235628 Primes whose base-8 representation also is the base-5 representation of a prime.

2, 3, 17, 19, 73, 89, 131, 163, 257, 521, 577, 739, 1097, 1171, 1283, 1601, 1747, 2081, 2083, 2137, 2267, 4177, 4289, 4363, 4643, 5273, 5387, 5651, 5779, 5849, 5851, 5923, 6211, 6299, 6337, 8353, 8713, 8803, 8929, 8969, 8971, 9377, 9419, 9473, 9491, 9811, 9883, 10009

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..3395

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

Example

Both 17 = 23_8 and 23_5 = 13 are prime.

Prog

(PARI) is(p, b=5, c=8)=vecmax(d=digits(p, c))<b&&isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)
(PARI) forprime(p=1, 3e3, is(p, 8, 5)&&print1(vector(#d=digits(p, 5), i, 8^(#d-i))*d~, ", ")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(., 5, 8)

Crossrefs

Cf. A235632, 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: A051074 A051094 A154274 * A140834 A121409 A041295

Adjacent sequences: A235625 A235626 A235627 * A235629 A235630 A235631

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved