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Primes whose base-7 representation also is the base-4 representation of a prime.
2

%I #14 Nov 02 2023 10:39:35

%S 2,3,17,59,71,73,113,353,367,449,463,491,701,743,757,787,857,1039,

%T 1151,1193,2411,2423,2467,2551,2843,3109,3137,3209,3251,4817,4903,

%U 5209,5657,5839,5939,5953,7211,7603,7703,8009,8039,8291,8387,16831,16871,16927,17207,17321,17837,19211,19267,20261,20287,22123,22303

%N Primes whose base-7 representation also is the base-4 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 Robert Price, <a href="/A235617/b235617.txt">Table of n, a(n) for n = 1..8515</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., 17 = 23_7 and 23_4 = 11 are both prime.

%o (PARI) is(p,b=4,c=7)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)

%o (PARI) forprime(p=1,3e3,is(p,7,4)&&print1(vector(#d=digits(p,4),i,7^(#d-i))*d~,",")) \\ To produce the terms, this is more efficient than to select them using straightforwardly is(.)=is(.,4,9)

%Y Cf. A235634, 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