|
%I #18 Jan 16 2022 23:21:05
%S 2,3,5,17,47,71,97,101,131,157,173,191,211,251,257,277,307,311,353,
%T 367,401,421,461,487,491,563,577,601,631,643,647,683,701,743,751,761,
%U 853,857,907,911,937,953,983,1021,1033,1087,1103,1193,1201,1259,1277,1289,1327,1451,1471,1571,1583,1597,1601,1747,1831,1907,1933
%N Primes whose base-6 representation is also the base-7 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.
%H Harvey P. Dale, <a href="/A235636/b235636.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 17 = 25_6 and 25_7 = 19 are both prime.
%t Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,6],7]]&] (* _Harvey P. Dale_, Sep 17 2017 *)
%o (PARI) is(p,b=7,c=6)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y Cf. A235637, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Jan 13 2014
|
