A235475 - OEIS

%I #12 Apr 14 2021 01:17:19

%S 2,7,11,13,19,41,59,127,151,157,167,173,181,191,223,233,241,271,313,

%T 331,409,421,443,463,541,563,577,607,613,641,701,709,733,743,809,859,

%U 877,919,929,953,967,991,1021,1033,1069,1087,1193,1259,1373,1423,1451,1453,1471,1483,1493,1549,1697,1753,1759,1783,1787,1831,1877,1979,1993

%N Primes whose base-2 representation also is the base-5 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.

%H Harvey P. Dale, <a href="/A235475/b235475.txt">Table of n, a(n) for n = 1..1000</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 7 = 111_2 and 111_5 = 31 are both prime, so 7 is a term.

%t Select[Prime[Range[400]],PrimeQ[FromDigits[IntegerDigits[#,2],5]]&] (* _Harvey P. Dale_, Jun 15 2019 *)

%o (PARI) is(p,b=5,c=2)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ This code is only valid for b>c.

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

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 12 2014