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 A325197 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. 8
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The enumeration of these partitions by sum is given by A325199. LINKS Gus Wiseman, Young diagrams for their first 60 terms EXAMPLE 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} MATHEMATICA 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&] CROSSREFS Cf. A195086, A065770, A325166, A325168, A325169, A325170, A325180, A325182, A325188, A325189, A325195, A325196, A325198, A325199, A325200. Sequence in context: A314521 A314522 A314523 * A314524 A314525 A314526 Adjacent sequences:  A325194 A325195 A325196 * A325198 A325199 A325200 KEYWORD nonn AUTHOR Gus Wiseman, Apr 11 2019 STATUS approved

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Last modified November 28 20:15 EST 2020. Contains 338754 sequences. (Running on oeis4.)