A235634 Primes whose base-4 representation is also the base-7 representation of a prime.

2, 3, 11, 23, 29, 31, 41, 71, 79, 101, 109, 113, 137, 149, 157, 163, 191, 199, 239, 251, 263, 269, 283, 307, 353, 397, 401, 431, 443, 521, 547, 601, 701, 709, 743, 751, 773, 853, 887, 941, 947, 983, 1013, 1039, 1049, 1069, 1109, 1151, 1217, 1283, 1303, 1487, 1489, 1663, 1669, 1789, 1823, 1901, 1949, 1973

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

			E.g., 11 = 23_4 and 23_7 = 17 both are prime.
		

Links

• Robert Israel, 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. A235617, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971, A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.

Programs

Maple

filter:= proc(n) local L,m;
  if not isprime(n) then return false fi;
  L:= convert(n,base,4);
  isprime(add(L[i]*7^(i-1),i=1..nops(L)));
end proc:
select(filter, [2,seq(i,i=3..10000,2)]); # Robert Israel, Jul 02 2018

PARI

is(p,b=7,c=4)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.