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.

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

Offset

1,1

Comments

The enumeration of these partitions by sum is given by A325199.

Links

Table of n, a(n) for n=1..56.

FindStat, St000384: The maximal part of the shifted composition of an integer partition

FindStat, St000783: The maximal number of occurrences of a colour in a proper colouring of a Ferrers diagram

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 A357359 A314525

Adjacent sequences: A325194 A325195 A325196 * A325198 A325199 A325200

Keyword

nonn

Author

Gus Wiseman, Apr 11 2019

Status

approved