cp's OEIS Frontend

A235626 Primes whose base-6 representation also is the base-5 representation of a prime.

%I A235626 #13 Jan 16 2022 23:29:43
%S A235626 2,3,13,43,97,223,307,337,379,433,457,547,709,727,769,811,919,1009,
%T A235626 1303,1597,1609,1777,1861,1987,2017,2029,2221,2239,2269,2311,2647,
%U A235626 2689,2749,2917,3037,3067,3121,3169,3373,3529,3541,3571,3613,3967,4219,4261,4327,4339
%N A235626 Primes whose base-6 representation also is the base-5 representation of a prime.
%C A235626 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 A235626 Robert Israel, <a href="/A235626/b235626.txt">Table of n, a(n) for n = 1..10000</a>
%H A235626 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 A235626 Both 13 = 21_6 and 21_5 = 11 are prime.
%p A235626 P:= {seq(ithprime(i),i=1..10000)}:
%p A235626 f:= proc(p) local i,L;
%p A235626   L:= convert(p,base,5);
%p A235626   add(L[i]*6^(i-1),i=1..nops(L))
%p A235626 end proc:
%p A235626 sort(convert(map(f,P) intersect P,list)); # _Robert Israel_, Jun 18 2019
%t A235626 b65pQ[n_]:=Module[{idn6=IntegerDigits[n,6]},Max[idn6]<5&&PrimeQ[ FromDigits[ idn6,5]]]; Select[Prime[Range[600]],b65pQ] (* _Harvey P. Dale_, Oct 13 2020 *)
%o A235626 (PARI) is(p,b=5,c=6)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)
%o A235626 (PARI) forprime(p=1,3e3,is(p,6,5)&&print1(vector(#d=digits(p,5),i,6^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,4,6)
%Y A235626 Cf. A235625, A235265, A235266, A152079, A235461 - A235482, A065720 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235615 - A235639. See the LINK for further cross-references.
%K A235626 nonn,base
%O A235626 1,1
%A A235626 _M. F. Hasler_, Jan 13 2014