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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[1]:=0:T[1]:=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(ā€˜T[i]ā€™,ā€˜iā€™=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

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Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)