login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A205402 Least k such that n divides s(k)-s(j) for some j<k, where s(j)=floor[(j+1)^2/2] (quarter-squares). 9
2, 3, 3, 4, 4, 6, 5, 5, 8, 6, 6, 7, 9, 7, 7, 8, 11, 8, 8, 11, 9, 12, 9, 9, 14, 10, 11, 10, 10, 11, 14, 11, 12, 11, 11, 12, 13, 12, 15, 12, 12, 16, 13, 14, 13, 20, 13, 13, 19, 14, 17, 14, 20, 14, 14, 16, 21, 15, 25, 15, 17, 15, 15, 19, 17, 16, 28, 16, 17, 16, 16, 17, 26 (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..73.

MATHEMATICA

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

z1 = 1000; z2 = 80;

Table[s[n], {n, 1, 30}]   (* A002620, quarter-squares *)

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

Table[u[m], {m, 1, z1}]   (* A205400 *)

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}]   (* A205401 *)

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}]        (* A205402 *)

Table[j[n], {n, 1, z2}]        (* A205403 *)

Table[s[k[n]], {n, 1, z2}]     (* A205404 *)

Table[s[j[n]], {n, 1, z2}]     (* A205405 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205406 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A198293 *)

CROSSREFS

Cf. A000982, A205400, A204892.

Sequence in context: A164512 A127434 A266475 * A226107 A105677 A230476

Adjacent sequences:  A205399 A205400 A205401 * A205403 A205404 A205405

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 27 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 11:13 EST 2016. Contains 278750 sequences.