A161401 - OEIS

%I #21 Sep 08 2022 08:45:45

%S 13,17,31,37,71,73,79,97,101,103,104,106,107,109,110,113,118,119,124,

%T 125,127,128,130,131,133,136,137,139,140,142,146,149,152,157,160,163,

%U 164,167,169,170,172,173,175,176,179,181,182,190,191,193,194,196,197

%N Numbers n such that the count of primes among the permutations of the digits of n is greater than 1.

%C Leading zeros in the permutations are ignored.

%H Vincenzo Librandi, <a href="/A161401/b161401.txt">Table of n, a(n) for n = 1..4690</a>

%H Cino Hilliard, <a href="/A161401/a161401.txt">Comments and PARI program.</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%e 13 has two permutations of its digits 1, 3 that form a prime, namely 13, 31. So the count of primes for 13 is greater than 1 and 13 is in the sequence.

%t Select[Range[300], Count[FromDigits/@Permutations[IntegerDigits[#]],_?PrimeQ]>1&] (* _Vincenzo Librandi_, Feb 02 2018 *)

%o (PARI) See Hilliard link.

%o (Magma) [ n: n in [1..200] | #[ s: s in Seqset([ Seqint([m(p[i]):i in [1..#x] ], 10): p in Permutations(Seqset(x)) ]) | IsPrime(s) ] gt 1 where m is map< x->y | [<x[i],y[i]>:i in [1..#x] ] > where x is [1..#y] where y is Intseq(n,10) ]; // _Klaus Brockhaus_, Jun 14 2009

%Y Cf. A161402, A161403, A161404.

%K base,nonn

%O 1,1

%A _Cino Hilliard_, Jun 09 2009

%E Edited by _Klaus Brockhaus_, Jun 14 2009