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A325196
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Heinz numbers of integer partitions such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 1.
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9
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3, 4, 9, 10, 12, 15, 18, 20, 42, 45, 50, 60, 63, 70, 75, 84, 90, 100, 105, 126, 140, 150, 294, 315, 330, 350, 420, 441, 462, 490, 495, 525, 550, 588, 630, 660, 693, 700, 735, 770, 825, 882, 924, 980, 990, 1050, 1100, 1155, 1386, 1470, 1540, 1650, 2730, 3234
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OFFSET
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1,1
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COMMENTS
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The enumeration of these partitions by sum is given by A325191.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
3: {2}
4: {1,1}
9: {2,2}
10: {1,3}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
20: {1,1,3}
42: {1,2,4}
45: {2,2,3}
50: {1,3,3}
60: {1,1,2,3}
63: {2,2,4}
70: {1,3,4}
75: {2,3,3}
84: {1,1,2,4}
90: {1,2,2,3}
100: {1,1,3,3}
105: {2,3,4}
126: {1,2,2,4}
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MATHEMATICA
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primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
otbmax[ptn_]:=Max@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
Select[Range[1000], otbmax[primeptn[#]]-otb[primeptn[#]]==1&]
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CROSSREFS
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Cf. A060687, A065770, A256617, A325166, A325169, A325179, A325181, A325183, A325185, A325188, A325189, A325191, A325195, A325200.
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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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