A235624 Primes whose base-4 representation is also the base-6 representation of a prime.

2, 3, 5, 13, 17, 37, 61, 73, 109, 157, 173, 181, 229, 233, 241, 257, 317, 337, 349, 373, 397, 409, 541, 557, 569, 601, 613, 661, 761, 769, 797, 821, 857, 953, 1013, 1021, 1033, 1069, 1153, 1181, 1193, 1201, 1229, 1237, 1297, 1321, 1373, 1429, 1481, 1609, 1621, 1637, 1709, 1801, 1861, 1877, 1889, 1901, 1973

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

5 = 11_4 and 11_6 = 7 are both prime, so 5 is a term.

Mathematica

Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 4], 6] &] (* Giovanni Resta, Sep 12 2019 *)

Prog

(PARI) is(p, b=6, c=4)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

Crossrefs

Cf. A235616, 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: A066111 A065820 A163268 * A355518 A108562 A087523

Adjacent sequences: A235621 A235622 A235623 * A235625 A235626 A235627

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved