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Numbers n such that the count of primes among the permutations of the digits of n is greater than 3.
2

%I #16 Sep 08 2022 08:45:45

%S 107,149,170,179,194,197,379,397,419,491,701,709,710,719,739,790,791,

%T 793,907,914,917,937,941,970,971,973,1003,1007,1009,1012,1013,1015,

%U 1016,1018,1019,1021,1024,1028,1030,1031,1033,1036,1037,1039,1042,1049,1051

%N Numbers n such that the count of primes among the permutations of the digits of n is greater than 3.

%C Leading zeros in the permutations are ignored.

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

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

%e 107 has four permutations of its digits 1, 0, 7 that form a prime, namely 107, 017, 071, 701. So the count of primes for 107 is greater than 3 and 107 is in the sequence.

%t Select[Range[1100],Count[FromDigits/@Permutations[IntegerDigits[#]], _?PrimeQ]>3&] (* _Harvey P. Dale_, Mar 04 2013 *)

%o (PARI) See Hilliard link.

%o (Magma) [ n: n in [1..1060] | #[ s: s in Seqset([ Seqint([m(p[i]):i in [1..#x] ], 10): p in Permutations(Seqset(x)) ]) | IsPrime(s) ] gt 3 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. A161401, A161402, A161404.

%K base,nonn

%O 1,1

%A _Cino Hilliard_, Jun 09 2009

%E Edited by _Klaus Brockhaus_, Jun 14 2009