login
Primes whose decimal representations interpreted in base 11 are not prime.
3

%I #17 Sep 08 2022 08:45:13

%S 11,13,17,19,23,31,37,41,47,53,59,71,73,79,83,97,101,103,107,109,113,

%T 127,131,137,149,151,157,163,167,173,179,181,191,211,223,229,233,239,

%U 241,251,257,271,277,283,293,307,311,313,317,337,347,349,359,367,383

%N Primes whose decimal representations interpreted in base 11 are not prime.

%C A090862(A049084(a(n))) = 11.

%H Marius A. Burtea, <a href="/A091923/b091923.txt">Table of n, a(n) for n = 1..1045</a>

%e A000040(9)=23 in base 11 is 2*11^1 + 3*11^0 = 25 = 5^2, therefore 29 is a term.

%t Select[Prime@Range@80, ! PrimeQ@FromDigits[IntegerDigits@#, 11] &] (* _Vincenzo Librandi_, Jul 01 2019 *)

%o (Magma) [n:n in PrimesUpTo(400)| not IsPrime(Seqint(Intseq(n), 11))]; // _Marius A. Burtea_, Jun 30 2019

%o (PARI) isok(p) = isprime(p) && (d=digits(p)) && !isprime(fromdigits(d, 11)); \\ _Michel Marcus_, Jun 30 2019

%Y Cf. A091924.

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Feb 13 2004

%E Corrected by _Zak Seidov_, Feb 25 2004