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A325197
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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 2.
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8
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5, 8, 14, 21, 24, 25, 27, 28, 35, 36, 40, 54, 56, 66, 98, 99, 110, 120, 125, 132, 135, 147, 154, 165, 168, 175, 180, 189, 196, 198, 200, 220, 225, 231, 245, 250, 252, 264, 270, 275, 280, 297, 300, 308, 375, 378, 385, 390, 392, 396, 440, 450, 500, 546, 585, 594
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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 A325199.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
5: {3}
8: {1,1,1}
14: {1,4}
21: {2,4}
24: {1,1,1,2}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
35: {3,4}
36: {1,1,2,2}
40: {1,1,1,3}
54: {1,2,2,2}
56: {1,1,1,4}
66: {1,2,5}
98: {1,4,4}
99: {2,2,5}
110: {1,3,5}
120: {1,1,1,2,3}
125: {3,3,3}
132: {1,1,2,5}
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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[#]]==2&]
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CROSSREFS
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Cf. A195086, A065770, A325166, A325168, A325169, A325170, A325180, A325182, A325188, A325189, A325195, A325196, A325198, A325199, 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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