cp's OEIS Frontend

A231474 Primes whose base-3 representation is also the base-5 representation of a prime.

%I A231474 #20 Jan 16 2022 23:08:03
%S A231474 2,3,5,7,13,17,29,31,37,41,59,67,79,97,101,109,113,137,139,149,151,
%T A231474 173,181,193,223,229,251,269,271,293,311,331,353,367,373,379,383,389,
%U A231474 397,401,457,467,491,503,617,631,641,647,653,673,701,773,787,797,809,829,853,857,911,929,953,977
%N A231474 Primes whose base-3 representation is also the base-5 representation of a prime.
%C A231474 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 A231474 Giovanni Resta, <a href="/A231474/b231474.txt">Table of n, a(n) for n = 1..10000</a>
%H A231474 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 A231474 7 = 21_3 and 21_5 = 11 are both prime, so 7 is a term.
%t A231474 Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 3], 5] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o A231474 (PARI) is(p,b=5,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y A231474 Cf. A235265, A235266, A235473, A152079, A235461 - A235482, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924. See the LINK for further cross-references.
%K A231474 nonn,base
%O A231474 1,1
%A A231474 _M. F. Hasler_, Jan 12 2014