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A205002 Least k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=j(j+1)/2. 8
2, 2, 3, 4, 3, 5, 4, 8, 4, 6, 6, 5, 7, 5, 6, 16, 9, 6, 10, 6, 8, 7, 12, 9, 7, 8, 7, 11, 15, 8, 16, 32, 8, 10, 8, 12, 19, 11, 9, 10, 21, 9, 22, 9, 10, 13, 24, 17, 10, 12, 11, 10, 27, 10, 13, 11, 12, 16, 30, 11, 31, 17, 11, 64, 11, 17, 34, 12, 14, 13, 36, 12, 37, 20, 12, 13, 12, 18, 40, 18, 13, 22, 42, 14, 13, 23, 17, 13, 45, 13, 16, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A204892 for a discussion and guide to related sequences.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..11001

EXAMPLE

(See example at A205001.)

MATHEMATICA

s[n_] := s[n] = Binomial[n + 1, 2]; z1 = 500; z2 = 60;

Table[s[n], {n, 1, 30}]  (* A000217 *)

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

Table[u[m], {m, 1, z1}]  (* A193974 ? *)

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}]      (* A205001 *)

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}]      (* A205002 *)

Table[j[n], {n, 1, z2}]      (* A205003 *)

Table[s[k[n]], {n, 1, z2}]   (* A205004 *)

Table[s[j[n]], {n, 1, z2}]   (* A205005 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205006 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205007 *)

PROG

(PARI) A205002(n) = for(k=2, oo, my(sk=binomial(k+1, 2)); for(j=1, k-1, if(!((sk-binomial(j+1, 2))%n), return(k)))); \\ Antti Karttunen, Sep 27 2018

CROSSREFS

Cf. A000217, A204892, A193974, A205006, A205007.

Sequence in context: A091525 A091524 A026350 * A290735 A165634 A128282

Adjacent sequences:  A204999 A205000 A205001 * A205003 A205004 A205005

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 21 2012

EXTENSIONS

More terms from Antti Karttunen, Sep 27 2018

STATUS

approved

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)