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A324170
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Numbers whose multiset multisystem (A302242) is crossing.
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29
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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}}
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MATHEMATICA
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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[#]]&]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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