|
%I #18 Jan 17 2022 00:32:34
%S 2,3,5,7,17,37,53,79,89,109,127,223,263,277,367,389,433,439,457,479,
%T 521,541,577,593,709,727,757,911,953,967,983,1061,1097,1117,1151,1153,
%U 1297,1447,1567,1583,1601,1637,1693,1709,1801,1879,1933,1951,2017,2069,2081,2213,2269
%N Primes whose base-8 representation is also the base-9 representation of a prime.
%C This sequence is part of a two-dimensional array of sequences, given in the LINK, 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 Giovanni Resta, <a href="/A231480/b231480.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 17 = 21_8 and 21_9 = 19 are both prime, so 17 is a term.
%t Select[Prime@ Range@ 500, PrimeQ@ FromDigits[ IntegerDigits[#, 8], 9] &] (* _Giovanni Resta_, Sep 12 2019 *)
%o (PARI) is(p,b=9,c=8)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y Cf. A235620, 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
|
