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A324170
Numbers whose multiset multisystem (A302242) is crossing.
29
2117, 3973, 4234, 4843, 5183, 5249, 5891, 6351, 6757, 7181, 7801, 7946, 8249, 8468, 8903, 9193, 9686, 9727, 10019, 10063, 10366, 10498, 10585, 11051, 11513, 11567, 11782, 11857, 11919, 12557, 12629, 12702, 12851, 13021, 13193, 13459, 13514, 13631, 14123, 14362
OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset multisystem of n is obtained by taking the multiset of prime indices of each prime index of n.
A multiset of multisets is crossing if it contains a 2-element submultiset of the form {{...x...y...}, {...z...t...}} where x < z < y < t or z < x < t < y.
EXAMPLE
The sequence of terms together with their multiset multisystems begins:
2117: {{1,3},{2,4}}
3973: {{1,3},{2,5}}
4234: {{},{1,3},{2,4}}
4843: {{1,3},{2,6}}
5183: {{1,1,3},{2,4}}
5249: {{1,3},{1,2,4}}
5891: {{1,4},{2,5}}
6351: {{1},{1,3},{2,4}}
6757: {{1,3},{2,7}}
7181: {{1,4},{2,6}}
7801: {{1,3},{2,8}}
7946: {{},{1,3},{2,5}}
8249: {{2,4},{1,2,3}}
8468: {{},{},{1,3},{2,4}}
8903: {{1,3},{2,2,4}}
9193: {{1,3},{1,2,5}}
9686: {{},{1,3},{2,6}}
9727: {{1,1,3},{2,5}}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
croXQ[stn_]:=MatchQ[stn, {___, {___, x_, ___, y_, ___}, ___, {___, z_, ___, t_, ___}, ___}/; x<z<y<t||z<x<t<y];
Select[Range[10000], croXQ[primeMS/@primeMS[#]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 17 2019
STATUS
approved