cp's OEIS Frontend

A235476 Primes whose base-2 representation also is the base-6 representation of a prime.

%I A235476 #12 Jan 03 2022 14:43:21
%S A235476 3,5,7,11,17,19,29,41,53,67,101,127,193,263,281,337,353,431,461,479,
%T A235476 487,499,523,593,599,631,743,757,773,821,823,829,857,883,887,941,1013,
%U A235476 1021,1093,1117,1259,1279,1303,1367,1373,1429,1439,1459,1471,1483,1493,1511,1583,1619,1699,1759,1831,1847,1879,1931,1951,1987
%N A235476 Primes whose base-2 representation also is the base-6 representation of a prime.
%C A235476 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 A235476 For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.
%H A235476 Harvey P. Dale, <a href="/A235476/b235476.txt">Table of n, a(n) for n = 1..1000</a>
%H A235476 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 A235476 5 = 101_2 and 101_6 = 37 are both prime, so 5 is a term.
%e A235476 7 = 111_2 and 111_6 = 43 are both prime, so 7 is a term.
%t A235476 Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,2],6]]&] (* _Harvey P. Dale_, Jan 03 2022 *)
%o A235476 (PARI) is(p,b=6)=isprime(vector(#d=binary(p),i,b^(#d-i))*d~)&&isprime(p)
%Y A235476 Cf. A235463 ⊂ A077720, A235475, A152079, A235266, A065720 ⊂ A036952, A065721 - A065727, A089971 ⊂ A020449, A089981, A090707 - A091924, A235394, A235395, A235461 - A235482. See the LINK for further cross-references.
%K A235476 nonn,base
%O A235476 1,1
%A A235476 _M. F. Hasler_, Jan 12 2014