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A161404
Numbers having more than 7 primes among the permutations of their digits.
3
1013, 1031, 1039, 1049, 1079, 1093, 1094, 1097, 1103, 1123, 1130, 1132, 1139, 1193, 1213, 1231, 1237, 1273, 1279, 1297, 1301, 1309, 1310, 1312, 1319, 1321, 1327, 1349, 1367, 1372, 1376, 1390, 1391, 1394, 1409, 1439, 1457, 1475, 1478, 1487, 1490, 1493
OFFSET
1,1
COMMENTS
Leading zeros in the permutations are ignored.
LINKS
Wikipedia, Permutation
EXAMPLE
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.
MATHEMATICA
Select[Range[2000], Count[FromDigits/@Permutations[IntegerDigits[#]], _?PrimeQ]>7&] (* Vincenzo Librandi, Feb 02 2018 *)
PROG
(PARI) See Hilliard link.
(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
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Cino Hilliard, Jun 09 2009
EXTENSIONS
Edited by Klaus Brockhaus, Jun 14 2009
STATUS
approved