A235476 - OEIS

A235476

Primes whose base-2 representation also is the base-6 representation of a prime.

3, 5, 7, 11, 17, 19, 29, 41, 53, 67, 101, 127, 193, 263, 281, 337, 353, 431, 461, 479, 487, 499, 523, 593, 599, 631, 743, 757, 773, 821, 823, 829, 857, 883, 887, 941, 1013, 1021, 1093, 1117, 1259, 1279, 1303, 1367, 1373, 1429, 1439, 1459, 1471, 1483, 1493, 1511, 1583, 1619, 1699, 1759, 1831, 1847, 1879, 1931, 1951, 1987

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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.

For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

EXAMPLE

5 = 101_2 and 101_6 = 37 are both prime, so 5 is a term.

7 = 111_2 and 111_6 = 43 are both prime, so 7 is a term.

MATHEMATICA

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 2], 6]]&] (* Harvey P. Dale, Jan 03 2022 *)

PROG

(PARI) is(p, b=6)=isprime(vector(#d=binary(p), i, b^(#d-i))*d~)&&isprime(p)

CROSSREFS