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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 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 September 27 10:28 EDT 2021. Contains 347689 sequences. (Running on oeis4.)