

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
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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 nth 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(āT[i]ā, āiā=1..n0):
for p from 1 to 12000 while(jj=0) do:
z1:=sqrt(5*(s+p)^2+4):z2:=sqrt(5*(s+p)^24):
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



