cp's OEIS Frontend

A235465 Primes whose base-8 representation also is the base-2 representation of a prime.

%I A235465 #12 Apr 14 2021 01:17:15
%S A235465 73,521,577,4673,32833,33289,33353,36929,37441,262153,262217,262657,
%T A235465 295433,2097673,2101313,2359369,2363401,2392073,16777289,16810049,
%U A235465 16814089,16814153,16814657,17039881,17043977,17076809,18874433,18907201,19137089,19140617,134222401,134483969,134484481,134513161
%N A235465 Primes whose base-8 representation also is the base-2 representation of a prime.
%C A235465 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 A235465 For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
%C A235465 When the smaller base is b=2 such that only digits 0 and 1 are allowed, these are primes that are the sum of distinct powers of the larger base, here c=8, thus a subsequence of A077722.
%H A235465 Alois P. Heinz, <a href="/A235465/b235465.txt">Table of n, a(n) for n = 1..10000</a>
%H A235465 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 A235465 73 = 111_8 and 111_2 = 7 are both prime, so 73 is a term.
%o A235465 (PARI) is(p,b=2,c=8)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o A235465 (PARI) forprime(p=1,1e3,is(p,8,2)&&print1(vector(#d=digits(p,2),i,8^(#d-i))*d~,",")) \\ To produce the terms, this is much more efficient than to select them using straightforwardly is(.)=is(.,2,8)
%Y A235465 Cf. A235478, A235479, A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.
%K A235465 nonn,base
%O A235465 1,1
%A A235465 _M. F. Hasler_, Jan 11 2014