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

Author

Franklin T. Adams-Watters, Nov 28 2011

Keywords

• nonn

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)

Crossrefs

Cf. A051683, A034968.

Partial sums of A130493.

Programs

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 *)

PARI

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

Formula

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