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Primes whose base-6 representation also is the base-3 representation of a prime.
2

%I #15 Nov 01 2023 23:21:00

%S 2,13,43,73,223,1777,2593,2887,3037,3067,3109,7993,9157,9337,10597,

%T 17077,17107,17137,17317,17359,18229,18661,46663,48247,49297,49537,

%U 54517,54727,54877,54907,54949,55987,56197,56209,56239,57097,63589,63727,64879,65089,65101,95089,95917,96157

%N Primes whose base-6 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="/A235469/b235469.txt">Table of n, a(n) for n = 1..1959</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 E.g., 13 = 21_6 and 21_3 = 7 are both prime.

%o (PARI) is(p,b=3,c=6)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)

%o (PARI) forprime(p=1,1e3,is(p,6,3)&&print1(vector(#d=digits(p,3),i,6^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,3,6)

%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