A231479 Primes whose base-7 representation is also the base-9 representation of a prime.

2, 3, 5, 11, 19, 23, 29, 37, 47, 67, 71, 89, 103, 107, 113, 127, 137, 163, 179, 239, 257, 313, 337, 347, 389, 401, 431, 457, 463, 499, 523, 547, 569, 571, 617, 709, 719, 739, 743, 751, 757, 761, 821, 823, 859, 883, 887, 971, 1019, 1069, 1093, 1129, 1153, 1213, 1297, 1307, 1327, 1367, 1373, 1381

Offset: 1

Author

M. F. Hasler, Jan 12 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

			11 = 14_7 and 14_9 = 13 are both prime, so 11 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. A235621, A235265, A235266, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime@ Range@ 250, PrimeQ@ FromDigits[IntegerDigits[#, 7], 9] &] (* Giovanni Resta, Sep 12 2019 *)

PARI

is(p,b=9,c=7)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.