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A061836 a(n) = smallest k>0 such that k+n divides k!. 12
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, 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, 8, 7, 6, 13, 12, 11, 10, 9, 8, 7, 6, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Comments from M. F. Hasler, Feb 20 2020 (Start)
The index at which any n > 2 appears for the last time is given by A005096(n) = n! - n.
For m>2, a(n) > m for n > A005096(m).
The integer 1 appears only once as a(0), the integer 2 is the only positive integer which never appears. (End)
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
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
LINKS
J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, Three Cousins of Recaman's Sequence, arXiv:2004:14000 [math.NT], April 2020.
MATHEMATICA
f[n_] := (k = 1; While[ !IntegerQ[ k! / (k + n) ], k++ ]; k); Table[ f[n], {n, 0, 75} ]
PROG
(PARI) a(n) = my (f=1); for (k=1, oo, if ((f*=k)%(n+k)==0, return (k))) \\ Rémy Sigrist, Feb 17 2020
CROSSREFS
Cf. A332584 for a "concatenation in base 10" variant.
See also A005096, A332558 (essentially identical to this one).
For records, see A333532 and A333533 (and A333537).
Sequence in context: A321028 A351169 A263356 * A021188 A334337 A370562
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jun 22 2001
EXTENSIONS
"k>0" added to definition at the suggestion of Chai Wah Wu, Apr 09 2020. - N. J. A. Sloane, Apr 22 2020
STATUS
approved

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Last modified April 25 11:06 EDT 2024. Contains 371967 sequences. (Running on oeis4.)