

A325170


Heinz numbers of integer partitions with origintoboundary graphdistance equal to 2.


10



6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 25, 26, 27, 28, 33, 34, 35, 36, 38, 39, 40, 44, 46, 48, 49, 51, 52, 54, 55, 56, 57, 58, 62, 65, 68, 69, 72, 74, 76, 77, 80, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 104, 106, 108, 111, 112, 115, 116, 118, 119
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OFFSET

1,1


COMMENTS

The origintoboundary graphdistance of a Young diagram is the minimum number of unit steps East or South from the upperleft square to a nonsquare in the lowerright quadrant. It is also the sidelength 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

Table of n, a(n) for n=1..63.
Gus Wiseman, Young diagrams corresponding to the first 50 terms.


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

Cf. A001221, A001222, A006918, A056239, A065770, A112798, A174090, A257990, A297113, A325167, A325169.
Sequence in context: A091886 A333357 A111774 * A325229 A036347 A129492
Adjacent sequences: A325167 A325168 A325169 * A325171 A325172 A325173


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 05 2019


STATUS

approved



