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A205394 Least k such that n divides s(k)-s(j) for some j<k, where s(j)=ceiling(j^2/2). 9
2, 3, 3, 3, 5, 4, 4, 5, 8, 6, 5, 5, 6, 8, 8, 6, 6, 9, 8, 7, 10, 12, 7, 7, 10, 14, 8, 9, 11, 8, 8, 10, 9, 18, 12, 9, 10, 20, 9, 9, 15, 10, 11, 13, 10, 24, 12, 10, 10, 15, 20, 15, 11, 12, 16, 11, 14, 30, 11, 11, 22, 32, 15, 12, 18, 14, 12, 19, 26, 12, 12, 13, 14, 38, 20, 21 (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..76.

MATHEMATICA

s[n_] := s[n] = Floor[(n^2 + 1)/2]; z1 = 800; z2 = 80;

Table[s[n], {n, 1, 30}]     (* A000982 *)

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

Table[u[m], {m, 1, z1}]     (* A205392 *)

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}]     (* A205393 *)

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}]         (* A205394 *)

Table[j[n], {n, 1, z2}]         (* A205395 *)

Table[s[k[n]], {n, 1, z2}]      (* A205396 *)

Table[s[j[n]], {n, 1, z2}]      (* A205397 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205398 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205399 *)

CROSSREFS

Cf. A000982, A204892, A205399.

Sequence in context: A076559 A102601 A092308 * A213617 A205778 A328972

Adjacent sequences:  A205391 A205392 A205393 * A205395 A205396 A205397

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 27 2012

STATUS

approved

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Last modified July 9 05:17 EDT 2020. Contains 335538 sequences. (Running on oeis4.)