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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
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, 36, 16, 602, 17, 75, 18, 978, 19, 120, 21, 1586, 23, 2583, 24, 4169, 25, 202, 26, 6752, 27, 10939, 28, 29, 327, 30, 31, 34, 35, 539, 37, 38, 39, 40, 934, 41, 42, 56, 43 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

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,...

LINKS

Table of n, a(n) for n=0..62.

EXAMPLE

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

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

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

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

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

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

MAPLE

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

for n from 2 to nn do:

ii:=0:

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

   if {k} intersect lst = {}

    then

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

    else

   fi:

  od:

   jj:=0:n0:=nops(lst):s:=s:=sum(ā€˜T[i]ā€™, ā€˜iā€™=1..n0):

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

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

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

       then

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

       else

      fi:

    od:

od:

print(T):

CROSSREFS

Cf. A000045.

Sequence in context: A259971 A091809 A110315 * A221183 A178174 A094744

Adjacent sequences:  A275674 A275675 A275676 * A275678 A275679 A275680

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 05 2016

STATUS

approved

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Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)