cp's OEIS Frontend

A235480 Primes whose base-3 representation is also the base-9 representation of a prime.

%I A235480 #15 Jan 16 2022 23:30:28
%S A235480 2,5,7,11,17,19,23,31,37,41,43,53,67,71,73,83,89,97,103,149,157,199,
%T A235480 239,251,257,271,277,293,307,313,331,337,359,383,397,421,431,433,499,
%U A235480 541,557,571,587,599,601,613,631,653,659,661,683,691,709,727,751,769,823,887,911,983,1009,1021,1031,1049,1051,1063,1129,1163,1217
%N A235480 Primes whose base-3 representation is also the base-9 representation of a prime.
%C A235480 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.
%C A235480 Appears to be a subsequence of A015919, A045344, A052085, A064555 and A143578.
%H A235480 Giovanni Resta, <a href="/A235480/b235480.txt">Table of n, a(n) for n = 1..10000</a>
%H A235480 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 A235480 5 = 12_3 and 12_9 = 11 are both prime, so 5 is a term.
%t A235480 Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 3], 9] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o A235480 (PARI) is(p,b=9,c=3)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: Code only valid for b > c.
%Y A235480 Cf. A235265, A235473 - A235479, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.
%K A235480 nonn,base
%O A235480 1,1
%A A235480 _M. F. Hasler_, Jan 12 2014