A235473 Primes whose base-3 representation is also the base-4 representation of a prime.

2, 43, 61, 67, 97, 103, 127, 139, 151, 157, 199, 211, 229, 277, 283, 331, 337, 349, 373, 379, 433, 439, 463, 499, 523, 571, 601, 607, 727, 751, 787, 823, 853, 883, 919, 991, 1063, 1087, 1117, 1213, 1249, 1327, 1381, 1429, 1483, 1531, 1567, 1597, 1627, 1759, 1783, 1867, 1999

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.

This is a subsequence of A045331 and A045375.

Examples

			43 = 1121_3 and 1121_4 = 89 are both prime, so 43 is a term.
		

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

Crossrefs

Cf. A235266, A235474, A152079, A235475 - A235479, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

Programs

Mathematica

Select[Prime[Range[400]],PrimeQ[FromDigits[IntegerDigits[#,3],4]]&] (* Harvey P. Dale, Oct 16 2015 *)

PARI

is(p,b=4,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.