A366136 Contribution to the OEIS

 

A366136 Minimal number of factorials or their negatives that add to n. 2

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 (list; graph; refs; listen; history; edit; text; internal format)

OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 EXAMPLE 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. 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 *) CROSSREFS Cf. A000142, A034968, A366693. Sequence in context: A204018 A261915 A109037 * A366693 A147680 A192895 Adjacent sequences: A366133 A366134 A366135 * A366137 A366138 A366139 KEYWORD nonn,look AUTHOR James C. McMahon, Sep 30 2023 STATUS approved