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A235632

Primes whose base-5 representation is also the base-8 representation of a prime.

2, 3, 11, 13, 31, 41, 53, 73, 101, 131, 151, 223, 281, 313, 353, 401, 463, 521, 523, 541, 593, 661, 701, 733, 773, 941, 983, 1013, 1063, 1091, 1093, 1123, 1153, 1193, 1201, 1321, 1381, 1423, 1471, 1481, 1483, 1571, 1583, 1601, 1613, 1663, 1693, 1741, 1753, 1801, 1861, 1871, 1873

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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.

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

11 = 21_5 and 21_8 = 17 are both prime, so 11 is a term.

MATHEMATICA

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#, 5], 8]]&] (* Harvey P. Dale, Dec 15 2018 *)

PROG

(PARI) is(p, b=8, c=5)=isprime(vector(#d=digits(p, c), i, b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.

CROSSREFS