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A204932 Least k such that n divides k!-j! for some j satisfying 1<=j<k. 10
2, 3, 4, 3, 3, 4, 5, 5, 4, 6, 4, 5, 9, 6, 6, 5, 5, 4, 5, 6, 6, 4, 4, 5, 6, 9, 7, 8, 6, 6, 10, 5, 7, 6, 8, 7, 13, 5, 9, 6, 7, 6, 11, 7, 7, 8, 10, 5, 8, 6, 6, 9, 12, 7, 8, 8, 5, 6, 5, 6, 16, 10, 8, 9, 14, 7, 8, 11, 8, 8, 9, 7, 8, 13, 6, 7, 12, 9, 14, 7, 10, 7, 19, 8, 11, 11, 6, 7, 10, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A204892 for a discussion and guide to related sequences.

LINKS

Table of n, a(n) for n=1..90.

EXAMPLE

1 divides 2!-1!, so a(1)=2

2 divides 3!-2!, so a(2)=3

3 divides 4!-3!, so a(3)=4

13 divides 9!-4!, so a(13)=9

MATHEMATICA

s[n_] := s[n] = n!; z1 = 80; z2 = 60;

Table[s[n], {n, 1, 30}]     (* A000142 *)

u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]

Table[u[m], {m, 1, z1}]     (* A204930 *)

v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]

w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]

d[n_] := d[n] = First[Delete[w[n], Position[w[n], 0]]]

Table[d[n], {n, 1, z2}]     (* A204931 *)

k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]

m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]

j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2

Table[k[n], {n, 1, z2}]        (* A204932 *)

Table[j[n], {n, 1, z2}]        (* A204933 *)

Table[s[k[n]], {n, 1, z2}]     (* A204934 *)

Table[s[j[n]], {n, 1, z2}]     (* A204935 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204936 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A204937 *)

CROSSREFS

Cf. A000142, A204892.

Sequence in context: A322808 A119352 A205010 * A079086 A017839 A242294

Adjacent sequences:  A204929 A204930 A204931 * A204933 A204934 A204935

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 21 2012

STATUS

approved

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Last modified November 22 00:32 EST 2019. Contains 329383 sequences. (Running on oeis4.)