login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A205847 Numbers k for which 4 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number. 6
4, 6, 6, 7, 7, 7, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For a guide to related sequences, see A205840.
LINKS
EXAMPLE
The first six terms match these differences:
s(4)-s(1) = 5-1 = 4
s(6)-s(1) = 13-1 = 12
s(6)-s(4) = 13-5 = 8
s(7)-s(1) = 21-1 = 20
s(7)-s(4) = 21-5 = 16
s(7)-s(6) = 21-13 = 8
MATHEMATICA
s[n_] := s[n] = Fibonacci[n + 1]; z1 = 400; z2 = 60;
f[n_] := f[n] = Floor[(-1 + Sqrt[8 n - 7])/2];
Table[s[n], {n, 1, 30}]
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A204922 *)
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] = Delete[w[n], Position[w[n], 0]]
c = 4; t = d[c] (* A205846 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]] - 1])/2]
j[n_] := j[n] = t[[n]] - f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205847 *)
Table[j[n], {n, 1, z2}] (* A205848 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] * A205849 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205850 *)
CROSSREFS
Sequence in context: A035551 A087573 A201235 * A227967 A292672 A018937
KEYWORD
nonn
AUTHOR
Clark Kimberling, Feb 02 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)