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A235470 Primes whose base-7 representation also is the base-3 representation of a prime. 2

%I #19 Nov 02 2023 10:39:39

%S 2,7,107,401,443,457,701,743,751,2417,2753,2843,2851,3089,5147,5153,

%T 5503,16823,16921,17207,17257,17551,19553,19993,21617,21673,22003,

%U 22303,33623,33679,33721,34301,36017,36373,36457,38873,118057,118343,134507,134857,135151,137251,137593,140057

%N Primes whose base-7 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.

%C Since the trailing digit of the base-7 expansion must (like all others) be less than 3, this is a subsequence of A045381.

%H Robert Price, <a href="/A235470/b235470.txt">Table of n, a(n) for n = 1..829</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., 7 = 10_7 and 10_3 = 3 are both prime; 107 = 212_7 and 212_3 = 23 are both prime.

%o (PARI) is(p,b=3,c=7)=vecmax(d=digits(p,c))<b&&isprime(vector(#d,i,b^(#d-i))*d~)&&isprime(p)

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

%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

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)