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A235639 Primes whose base-9 representation is also the base-6 representation of a prime.

%I A235639 #21 May 18 2020 19:06:25
%S A235639 2,3,5,19,23,41,113,127,131,163,199,271,419,433,739,743,761,919,991,
%T A235639 1009,1013,1063,1153,1171,1459,1481,1499,1553,1567,1571,1733,1747,
%U A235639 1783,1873,1913,2237,2377,2381,2539,2557,2593,2633,2939,3011,3079,3083,3187,3259,3331,3659
%N A235639 Primes whose base-9 representation is also the base-6 representation of a prime.
%C A235639 This sequence is part of the two-dimensional array of sequences 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 A235639 Robert Israel, <a href="/A235639/b235639.txt">Table of n, a(n) for n = 1..10000</a>
%H A235639 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 A235639 19 = 21_9 and 21_6 = 13 are both prime, so 19 is a term.
%e A235639 509 = 625_9 and 625_6 = 17 are both prime, but 625 is not a valid base-6 integer, so 509 is not a term.
%p A235639 R:= 2: x:= 2: count:= 1:
%p A235639 while count < 100 do
%p A235639   x:= nextprime(x);
%p A235639   L:= convert(x,base,6);
%p A235639   y:= add(9^(i-1)*L[i],i=1..nops(L));
%p A235639   if isprime(y) then count:= count+1; R:= R, y fi
%p A235639 od:
%p A235639 R; # _Robert Israel_, May 18 2020
%o A235639 (PARI) is(p,b=6,c=9)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o A235639 (PARI) forprime(p=1,3e3,is(p,9,6)&&print1(vector(#d=digits(p,6),i,9^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,6,9)
%Y A235639 Cf. A231481, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235638. See the LINK for further cross-references.
%K A235639 nonn,base,look
%O A235639 1,1
%A A235639 _M. F. Hasler_, Jan 13 2014