A231476 - OEIS

A231476

Primes whose base-3 representation is also the base-6 representation of a prime.

2, 7, 13, 19, 31, 151, 163, 211, 223, 229, 241, 271, 349, 367, 439, 601, 607, 613, 631, 643, 673, 727, 733, 859, 907, 937, 997, 1021, 1033, 1039, 1051, 1093, 1117, 1123, 1129, 1153, 1321, 1327, 1399, 1423, 1429, 1609, 1627, 1657, 1669, 1741, 1747, 1759, 1777, 1789, 1831, 1867, 1933, 1951, 1993, 1999

(list; graph; refs; listen; history; text; internal format)

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.

Subsequence of A045375 ⊂ A045331.

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

7 = 21_3 and 21_6 = 13 are both prime.

MATHEMATICA

Select[Prime[Range[400]], PrimeQ[FromDigits[ IntegerDigits[#, 3], 6]] &] (* Harvey P. Dale, Sep 29 2016 *)

PROG

(PARI) is(p, b=6, c=3)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b>c.

CROSSREFS