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%I #35 Jul 19 2022 18:22:34
%S 0,1,3,5,11,17,23,47,71,95,119,239,359,479,599,719,1439,2159,2879,
%T 3599,4319,5039,10079,15119,20159,25199,30239,35279,40319,80639,
%U 120959,161279,201599,241919,282239,322559,362879,725759,1088639,1451519,1814399,2177279
%N Smallest number requiring n terms to be expressed as a sum of factorials.
%C Indices of record values in A034968.
%C Records for sum of digits when numbers are written in factorial base.
%C 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
%H Michael De Vlieger, <a href="/A200748/b200748.txt">Table of n, a(n) for n = 0..11324</a> (corresponding to rows 1 <= n <= 150 of A051683, see Formula)
%F a(n) = A051683(n+1) - 1.
%t 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 *)
%t Prepend[-1 + Rest@ Flatten[Table[n!*k, {n, 9}, {k, n}]], 0] (* _Michael De Vlieger_, Sep 03 2017, after _Jean-François Alcover_ at A051683 *)
%o (PARI) k=0;m=1;s=0;vector(45,n,s+=m!;if(k++==m,k=0;m++);s)
%Y Cf. A051683, A034968.
%Y Partial sums of A130493.
%K nonn
%O 0,3
%A _Franklin T. Adams-Watters_, Nov 28 2011
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