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Primes whose base-6 representation is also the base-9 representation of a prime.
2

%I #21 Jan 17 2022 00:28:02

%S 2,3,5,13,17,29,59,67,71,73,97,127,191,199,223,227,239,307,337,349,

%T 353,367,409,421,433,449,461,479,487,491,563,571,577,619,647,683,739,

%U 743,811,823,829,857,881,911,937,941,991,1021,1051,1091,1103,1117,1163,1201,1217,1259,1277,1289

%N Primes whose base-6 representation is also the base-9 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 Giovanni Resta, <a href="/A231481/b231481.txt">Table of n, a(n) for n = 1..10000</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 13 = 21_6 and 21_9 = 19 are both prime, so 13 is a term.

%t Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,6],9]]&] (* _Harvey P. Dale_, Aug 30 2015 *)

%o (PARI) is(p,b=9,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. A235639, 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