A200748 Smallest number requiring n terms to be expressed as a sum of factorials.

0, 1, 3, 5, 11, 17, 23, 47, 71, 95, 119, 239, 359, 479, 599, 719, 1439, 2159, 2879, 3599, 4319, 5039, 10079, 15119, 20159, 25199, 30239, 35279, 40319, 80639, 120959, 161279, 201599, 241919, 282239, 322559, 362879, 725759, 1088639, 1451519, 1814399, 2177279

Offset

0,3

Comments

Indices of record values in A034968.

Records for sum of digits when numbers are written in factorial base.

Numbers, n, whose factorial base representation digitally dominates every number less than or equal to n; we say n digitally dominates m if each digit of n in its factorial base representation is greater than or equal to the corresponding digit of m in its factorial base representation. - Joanne Beckford, Sep 01 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 0..11324 (corresponding to rows 1 <= n <= 150 of A051683, see Formula)

Formula

a(n) = A051683(n+1) - 1.

Mathematica

With[{b = MixedRadix[Reverse@ Range[2, 12]]}, Function[s, {0}~Join~Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]]@ Array[Total@ IntegerDigits[#, b] &, 10^5]] (* or *)
Prepend[-1 + Rest@ Flatten[Table[n!*k, {n, 9}, {k, n}]], 0] (* Michael De Vlieger, Sep 03 2017, after Jean-François Alcover at A051683 *)

Prog

(PARI) k=0; m=1; s=0; vector(45, n, s+=m!; if(k++==m, k=0; m++); s)

Crossrefs

Cf. A051683, A034968.

Partial sums of A130493.

Sequence in context: A155938 A158318 A099596 * A063693 A258713 A267517

Adjacent sequences: A200745 A200746 A200747 * A200749 A200750 A200751

Keyword

nonn

Author

Franklin T. Adams-Watters, Nov 28 2011

Status

approved