|
%I #19 Jan 16 2022 23:27:13
%S 2,3,11,13,31,41,53,73,101,131,151,223,281,313,353,401,463,521,523,
%T 541,593,661,701,733,773,941,983,1013,1063,1091,1093,1123,1153,1193,
%U 1201,1321,1381,1423,1471,1481,1483,1571,1583,1601,1613,1663,1693,1741,1753,1801,1861,1871,1873
%N Primes whose base-5 representation is also the base-8 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 Harvey P. Dale, <a href="/A235632/b235632.txt">Table of n, a(n) for n = 1..1000</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 11 = 21_5 and 21_8 = 17 are both prime, so 11 is a term.
%t Select[Prime[Range[300]],PrimeQ[FromDigits[IntegerDigits[#,5],8]]&] (* _Harvey P. Dale_, Dec 15 2018 *)
%o (PARI) is(p,b=8,c=5)=isprime(vector(#d=digits(p,c),i,b^(#d-i))*d~)&&isprime(p) \\ Note: This code is only valid for b > c.
%Y Cf. A235628, 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
|
