The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A275677 a(0)=0; for n > 0, a(n) is the least number not yet used having the property that a(n) added to the next n+1 terms is a Fibonacci number. 0

%I

%S 0,1,2,5,3,11,4,32,6,33,7,51,8,92,9,139,10,22,12,227,13,20,14,370,15,

%T 36,16,602,17,75,18,978,19,120,21,1586,23,2583,24,4169,25,202,26,6752,

%U 27,10939,28,29,327,30,31,34,35,539,37,38,39,40,934,41,42,56,43

%N a(0)=0; for n > 0, a(n) is the least number not yet used having the property that a(n) added to the next n+1 terms is a Fibonacci number.

%C The sequence a(n) is a permutation of the nonnegative integers.

%C The corresponding Fibonacci numbers are 1, 8, 21, 55, 89, 144, 233, 377, 377, 610, 610, 987, 987, 1597, 1597, 2584, 2584, 4181, 6765, 10946, 10946, 17711, 28657, 28657, 28657, 28657, 28657,...

%e Let F(n) the n-th Fibonacci number.

%e a(0)= 0 added to the next single term 1 is equal to F(1)=F(2)=1;

%e a(1)= 1 added to the next two terms (2,5) is equal to F(6)=8;

%e a(2)= 2 added to the next three terms (5,3,11) is equal to F(7)=21;

%e a(3)= 5 added to the next four terms (3,11,4,32) is equal to F(10)=55;

%e a(4)= 3 added to the next five terms (11,4,32,6,33) is equal to F(11)=89.

%p nn:=300:T:=array(1..nn):T:=0:T:=1:kk:=2:lst:={0, 1}:

%p for n from 2 to nn do:

%p ii:=0:

%p for k from 1 to 12000 while(ii=0)do:

%p if {k} intersect lst = {}

%p then

%p ii:=1:lst:=lst union {k}:kk:=kk+1:T[kk]:=k:

%p else

%p fi:

%p od:

%p jj:=0:n0:=nops(lst):s:=s:=sum(‘T[i]’,‘i’=1..n0):

%p for p from 1 to 12000 while(jj=0) do:

%p z1:=sqrt(5*(s+p)^2+4):z2:=sqrt(5*(s+p)^2-4):

%p if (z1=floor(z1) or z2=floor(z2)) and {p} intersect lst={}

%p then

%p jj:=1:lst:=lst union {p}:kk:=kk+1:T[kk]:=p:

%p else

%p fi:

%p od:

%p od:

%p print(T):

%Y Cf. A000045.

%K nonn

%O 0,3

%A _Michel Lagneau_, Aug 05 2016

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

Last modified October 19 11:16 EDT 2021. Contains 348088 sequences. (Running on oeis4.)