cp's OEIS Frontend

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

%I A235634 #16 Jan 16 2022 23:26:48
%S A235634 2,3,11,23,29,31,41,71,79,101,109,113,137,149,157,163,191,199,239,251,
%T A235634 263,269,283,307,353,397,401,431,443,521,547,601,701,709,743,751,773,
%U A235634 853,887,941,947,983,1013,1039,1049,1069,1109,1151,1217,1283,1303,1487,1489,1663,1669,1789,1823,1901,1949,1973
%N A235634 Primes whose base-4 representation is also the base-7 representation of a prime.
%C A235634 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.
%H A235634 Robert Israel, <a href="/A235634/b235634.txt">Table of n, a(n) for n = 1..10000</a>
%H A235634 M. F. Hasler, <a href="https://docs.google.com/document/d/10IM7fcAbB2tqRGuwfGvuEGUzD_IXbgXPDK0tfxN4M3o/pub">Primes whose base c expansion is also the base b expansion of a prime</a>
%e A235634 E.g., 11 = 23_4 and 23_7 = 17 both are prime.
%p A235634 filter:= proc(n) local L,m;
%p A235634   if not isprime(n) then return false fi;
%p A235634   L:= convert(n,base,4);
%p A235634   isprime(add(L[i]*7^(i-1),i=1..nops(L)));
%p A235634 end proc:
%p A235634 select(filter, [2,seq(i,i=3..10000,2)]); # _Robert Israel_, Jul 02 2018
%o A235634 (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.
%Y A235634 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.
%K A235634 nonn,base
%O A235634 1,1
%A A235634 _M. F. Hasler_, Jan 13 2014