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

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

Cf. A235628, 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: A078763 A157884 A234530 * A085306 A161322 A123239

Adjacent sequences: A235629 A235630 A235631 * A235633 A235634 A235635

Keyword

nonn,base

Author

M. F. Hasler, Jan 13 2014

Status

approved