OFFSET
1,1
COMMENTS
The origin-to-boundary graph-distance of a Young diagram is the minimum number of unit steps East or South from the upper-left square to a nonsquare in the lower-right quadrant. It is also the side-length of the minimum triangular partition contained inside the diagram.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
6: {1,2}
9: {2,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
25: {3,3}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
33: {2,5}
34: {1,7}
35: {3,4}
36: {1,1,2,2}
38: {1,8}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&, Append[ptn, 0]];
Select[Range[200], otb[Reverse[primeMS[#]]]==2&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2019
STATUS
approved