A231480 Primes whose base-8 representation is also the base-9 representation of a prime.

2, 3, 5, 7, 17, 37, 53, 79, 89, 109, 127, 223, 263, 277, 367, 389, 433, 439, 457, 479, 521, 541, 577, 593, 709, 727, 757, 911, 953, 967, 983, 1061, 1097, 1117, 1151, 1153, 1297, 1447, 1567, 1583, 1601, 1637, 1693, 1709, 1801, 1879, 1933, 1951, 2017, 2069, 2081, 2213, 2269

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

			17 = 21_8 and 21_9 = 19 are both prime, so 17 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. A235620, 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[#, 8], 9] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=9,c=8)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.