A235468 - OEIS

%I #17 Nov 01 2023 23:21:09

%S 2,5,7,11,31,37,127,131,151,157,257,281,311,661,677,751,757,877,881,

%T 907,911,1277,1301,1381,1511,1531,3137,3187,3251,3307,3407,3761,3877,

%U 3911,3931,4001,4007,4027,4051,4057,4561,4637,6257,6287,7057,7151,7177,7187,7507

%N Primes whose base-5 representation also is the base-3 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.

%C For further motivation and cross-references, see sequence A235265 which is the main entry for this whole family of sequences.

%H Robert Price, <a href="/A235468/b235468.txt">Table of n, a(n) for n = 1..11369</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 a(1) = 5 = 10_5 and 10_3 = 3 are both prime.

%e a(2) = 7 = 12_5 and 12_3 = 5 are both prime.

%e a(3) = 11 = 21_5 and 21_3 = 7 are both prime.

%o (PARI) is(p,b=3,c=5)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)

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

%Y Cf. A065720 ⊂ A036952, A065721 - A065727, A235394, A235395, A089971 ⊂ A020449, A089981, A090707 - A091924, A235461 - A235482. See the LINK for further cross-references.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Jan 12 2014