cp's OEIS Frontend

A235472 Primes whose base-9 representation also is the base-3 representation of a prime.

%I A235472 #9 Jan 16 2022 23:31:25
%S A235472 2,11,19,83,101,163,173,739,811,821,829,911,1549,1559,1621,6563,6581,
%T A235472 6661,6733,8111,8191,13933,14753,59069,59141,59779,59797,59951,60589,
%U A235472 60607,65629,65701,66359,67079,67231,72271,72353,72901,118189,119557,119657,124669,124823,125399
%N A235472 Primes whose base-9 representation also is the base-3 representation of a prime.
%C A235472 This sequence is part of the two-dimensional array of sequences 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 A235472 For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
%C A235472 Since all digits of the base 9 expansion are less than 3, this is a subsequence of A037314.
%H A235472 Alois P. Heinz, <a href="/A235472/b235472.txt">Table of n, a(n) for n = 1..10000</a>
%H A235472 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 A235472 Both 17 = 21_9 and 21_3 = 7 are prime.
%o A235472 (PARI) is(p,b=3,c=9)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o A235472 (PARI) forprime(p=1,2e3,is(p,9,3)&&print1(vector(#d=digits(p,3),i,9^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,3,9)
%Y A235472 Cf. A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.
%K A235472 nonn,base
%O A235472 1,1
%A A235472 _M. F. Hasler_, Jan 12 2014