A235481 Primes whose base-4 representation is also the base-9 representation of a prime.

2, 3, 29, 41, 61, 89, 109, 149, 157, 281, 293, 313, 401, 421, 433, 593, 701, 709, 1013, 1049, 1061, 1069, 1097, 1117, 1277, 1289, 1301, 1553, 1601, 1709, 2069, 2137, 2237, 2309, 2377, 2437, 2477, 2689, 2729, 2749, 2797, 2957, 2969, 3001, 3061, 3109, 3169, 3329, 3361, 3389, 3457, 3533, 3701

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.

Appears to be a subsequence of A197636.

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

29 = 131_4 and 131_9 = 109 are both prime, so 29 is a term.

Mathematica

Select[Prime@Range@600, PrimeQ[FromDigits[IntegerDigits[#, 4], 9]] &] (* Giovanni Resta, Sep 12 2019 *)

Prog

(PARI) is(p, b=9, c=4)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: Code only valid for b > c.

Crossrefs

Cf. A235473 - A235480, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

Sequence in context: A141192 A215135 A059453 * A214889 A137472 A065932

Adjacent sequences: A235478 A235479 A235480 * A235482 A235483 A235484

Keyword

nonn,base

Author

M. F. Hasler, Jan 12 2014

Status

approved