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A205018 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=j*(j+1). 9
2, 2, 3, 2, 3, 3, 4, 4, 4, 3, 6, 5, 7, 4, 6, 8, 9, 4, 10, 6, 8, 6, 12, 5, 7, 7, 7, 5, 15, 6, 16, 16, 8, 9, 8, 6, 19, 10, 9, 6, 21, 8, 22, 7, 10, 12, 24, 9, 10, 7, 11, 8, 27, 7, 13, 11, 12, 15, 30, 8 (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..60.

MATHEMATICA

s[n_] := s[n] = n*(n + 1); z1 = 500; z2 = 60;

Table[s[n], {n, 1, 30}]   (* A002378 *)

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

Table[u[m], {m, 1, z1}]   (* A205016 *)

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}]   (* A205017 *)

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}]      (* A205018 *)

Table[j[n], {n, 1, z2}]      (* A205028 *)

Table[s[k[n]], {n, 1, z2}]   (* A205029 *)

Table[s[j[n]], {n, 1, z2}]   (* A205030 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205031 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205032 *)

CROSSREFS

Cf. A002378, A204892, A205016.

Sequence in context: A303297 A107452 A349198 * A286716 A029213 A029209

Adjacent sequences:  A205015 A205016 A205017 * A205019 A205020 A205021

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 22 2012

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)