A366136 Minimal number of factorials or their negatives that add to n.

0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 4, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 4, 4, 3, 4, 4, 4, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 5, 4, 5, 5, 6, 5, 5, 4, 5, 5, 5, 4, 4, 3, 4, 4, 5, 5, 5, 4, 5, 5, 6, 5, 5, 4, 5, 5

Offset: 0

Author

James C. McMahon, Sep 30 2023

Keywords

• nonn
• look

Examples

			11 = 6 + 6 - 1 (three factorials), so a(11) = 3.
15 = 6 + 6 + 2 + 1 or 15 = 24 - 6 - 2 - 1 (four factorials), so a(15) = 4.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000142, A034968, A366693.

Programs

Mathematica

seq[m_] := Module[{s = Table[m!, {m!}], d, b, sum}, Do[d = PadLeft[Most@ IntegerDigits[k, MixedRadix[Range[m, 1, -1]]], m]; Do[b = 2*PadLeft[ IntegerDigits[i, 2], m] - 1; sum = Total[b * d * Range[m, 1, -1]!]; If[0 < sum <= m!, s[[sum]] = Min[s[[sum]], Total[d]]], {i, 1, 2^m - 1}], {k, 1, 2*m!}]; Join[{0}, s]]; seq[5] (* Amiram Eldar, Oct 03 2023 *)