This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061836 #46 Apr 26 2021 06:30:22
%S A061836 1,5,4,3,4,5,6,5,4,6,5,7,6,7,6,5,8,7,6,5,4,7,8,7,6,5,9,8,7,7,6,9,8,7,
%T A061836 6,5,9,8,7,6,8,7,6,11,10,9,10,9,8,7,10,9,8,7,6,5,7,13,12,11,10,9,8,7,
%U A061836 8,7,6,13,12,11,10,9,8,7,6,9
%N A061836 a(n) = smallest k>0 such that k+n divides k!.
%C A061836 Comments from _M. F. Hasler_, Feb 20 2020 (Start)
%C A061836 The index at which any n > 2 appears for the last time is given by A005096(n) = n! - n.
%C A061836 For m>2, a(n) > m for n > A005096(m).
%C A061836 The integer 1 appears only once as a(0), the integer 2 is the only positive integer which never appears. (End)
%C A061836 It would be nice to have an estimate for the growth of the upper envelope of this sequence - what is lim sup a(n)? The answer seems to be controlled by A333537. - _N. J. A. Sloane_, Apr 12 2020
%C A061836 _Paul Zimmermann_ suggests that perhaps a(n) is O(log(n)^2). My estimate was n^(1/3), although that seems a bit low. - _N. J. A. Sloane_, Apr 09 2020
%H A061836 Rémy Sigrist, <a href="/A061836/b061836.txt">Table of n, a(n) for n = 0..10000</a>
%H A061836 J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000 [math.NT], April 2020.
%H A061836 N. J. A. Sloane, <a href="/A061836/a061836.txt">Table of n, a(n) for n = 0..100000</a>
%t A061836 f[n_] := (k = 1; While[ !IntegerQ[ k! / (k + n) ], k++ ]; k); Table[ f[n], {n, 0, 75} ]
%o A061836 (PARI) a(n) = my (f=1); for (k=1, oo, if ((f*=k)%(n+k)==0, return (k))) \\ _Rémy Sigrist_, Feb 17 2020
%Y A061836 Cf. A332584 for a "concatenation in base 10" variant.
%Y A061836 See also A005096, A332558 (essentially identical to this one).
%Y A061836 For records, see A333532 and A333533 (and A333537).
%K A061836 nonn
%O A061836 0,2
%A A061836 _Robert G. Wilson v_, Jun 22 2001
%E A061836 "k>0" added to definition at the suggestion of _Chai Wah Wu_, Apr 09 2020. - _N. J. A. Sloane_, Apr 22 2020