%I #12 Nov 30 2022 12:20:39

%S 2,3,11,19,29,31,101,109,181,191,199,281,337,739,751,769,811,821,839,

%T 919,929,991,1459,1489,1549,1721,1741,1811,2269,2281,2371,2389,2441,

%U 2459,2531,2539,2551,2953,3089,3109,3251,3271,6571,6599,6661,6907,7309,7321,7489,7537,8039

%N Primes whose base-9 representation also is the base-5 representation of a prime.

%C 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 Alois P. Heinz, <a href="/A235629/b235629.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 Both 11 = 12_9 and 12_5 = 7 are prime.

%t pr95Q[n_]:=Module[{idn9=IntegerDigits[n,9]},Max[idn9]<5&&PrimeQ[ FromDigits[ idn9,5]]]; Select[Prime[Range[1100]],pr95Q] (* _Harvey P. Dale_, Nov 30 2022 *)

%o (PARI) is(p,b=5,c=9)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)

%o (PARI) forprime(p=1,3e3,is(p,9,5)&&print1(vector(#d=digits(p,5),i,9^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,5,9)

%Y Cf. A235482, 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