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%I #17 Sep 08 2022 08:45:45
%S 1013,1031,1039,1049,1079,1093,1094,1097,1103,1123,1130,1132,1139,
%T 1193,1213,1231,1237,1273,1279,1297,1301,1309,1310,1312,1319,1321,
%U 1327,1349,1367,1372,1376,1390,1391,1394,1409,1439,1457,1475,1478,1487,1490,1493
%N Numbers having more than 7 primes among the permutations of their digits.
%C Leading zeros in the permutations are ignored.
%H Vincenzo Librandi, <a href="/A161404/b161404.txt">Table of n, a(n) for n = 1..5200</a>
%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 1013 has eight permutations of its digits 1, 0, 1, 3 that form a prime, namely 113, 131, 311, 1013, 1031, 1103, 1301, 3011. So the count of primes for 1013 is greater than 7 and 1013 is in the sequence.
%t Select[Range[2000], Count[FromDigits/@Permutations[IntegerDigits[#]],_?PrimeQ]>7&] (* _Vincenzo Librandi_, Feb 02 2018 *)
%o (PARI) See Hilliard link.
%o (Magma) [ n: n in [1..1500] | #[ s: s in Seqset([ Seqint([m(p[i]):i in [1..#x] ], 10): p in Permutations(Seqset(x)) ]) | IsPrime(s) ] gt 7 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, A161403.
%K base,nonn
%O 1,1
%A _Cino Hilliard_, Jun 09 2009
%E Edited by _Klaus Brockhaus_, Jun 14 2009
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