A235633 Primes whose base-4 representation is also the base-8 representation of a prime.

2, 3, 7, 11, 19, 29, 37, 59, 71, 89, 97, 107, 149, 167, 223, 227, 251, 281, 337, 347, 439, 461, 463, 491, 499, 509, 521, 563, 599, 617, 647, 653, 659, 701, 727, 733, 739, 751, 757, 769, 797, 809, 823, 877, 887, 907, 911, 929, 937, 1031, 1087, 1093, 1109, 1163, 1187, 1193, 1297

Offset: 1

Author

M. F. Hasler, Jan 13 2014

Keywords

• nonn
• base

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.

Examples

			7 = 13_4 and 13_8 = 11 are both prime, so 7 is a term.
		

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

Crossrefs

Cf. A235618, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime@Range@500, PrimeQ@ FromDigits[IntegerDigits[#, 4], 8] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=8,c=4)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.