A235630 Primes whose base-7 representation is also the base-8 representation of a prime.

2, 3, 5, 17, 47, 71, 89, 101, 197, 229, 241, 269, 271, 337, 353, 383, 479, 521, 577, 607, 631, 647, 673, 677, 719, 743, 761, 827, 997, 1097, 1153, 1181, 1193, 1279, 1289, 1303, 1319, 1447, 1543, 1601, 1697, 1811, 1823, 1907, 1951, 1993, 2017, 2131, 2203, 2243, 2339, 2357, 2383, 2549

Offset

1,1

Comments

This sequence is part of a two-dimensional array of sequences, given in the LINK, 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

Giovanni Resta, Table of n, a(n) for n = 1..10000

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

Example

17 = 23_7 and 23_8 = 19 are both prime, so 17 is a term.

Mathematica

Select[Prime@Range@500, PrimeQ@ FromDigits[IntegerDigits[#, 7], 8] &] (* Giovanni Resta, Sep 12 2019 *)

Prog

(PARI) is(p, b=8, c=7)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

Crossrefs

Cf. A235622, 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: A243441 A256426 A019350 * A235636 A268130 A103074

Adjacent sequences: A235627 A235628 A235629 * A235631 A235632 A235633

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved