A235478 - OEIS

%I #17 Nov 01 2023 23:21:14

%S 7,11,13,29,37,43,47,53,61,67,71,73,107,139,149,199,211,227,263,293,

%T 307,311,317,331,347,383,389,421,461,467,541,593,601,619,641,643,739,

%U 811,863,907,937,1061,1069,1093,1117,1163,1223,1283,1301,1319,1321,1409,1433,1439,1489,1499,1523,1559,1619,1697,1811,1861,1879

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

%C 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 For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

%C Appears to be a subsequence of A050150, A062090 and A216285.

%H Robert Price, <a href="/A235478/b235478.txt">Table of n, a(n) for n = 1..2265</a>

%H 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 11 = 1011_2 and 1011_8 = 521 are both prime, so 11 is a term.

%t Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,2],8]]&] (* _Harvey P. Dale_, Sep 25 2015 *)

%o (PARI) is(p,b=8)=isprime(vector(#d=binary(p),i,b^(#d-i))*d~)&&isprime(p)

%Y Cf. A235465 ⊂ A077722, A235266, A152079, A235475 - A235479, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 12 2014