|
|
A269725
|
|
a(n) = row number of extended Wythoff array (see A035513) which contains the sequence n times the Fibonacci numbers 1,2,3,5,8,13,21,... .
|
|
10
|
|
|
0, 2, 3, 4, 15, 18, 21, 24, 27, 30, 33, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, 1113, 1134, 1155, 1176, 1197, 1218, 1239, 1260
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
REFERENCES
|
J. H. Conway, Posting to Math Fun Mailing List, Nov 25 1996.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Take n=5: 5 times 1,2,3,5,8,13,... gives 5,10,15,25,40,65,.., which is row 15 of the extended Wythoff array (when extended to the left), so a(5) = 15.
|
|
MAPLE
|
local f, sl, r, c, wrks ;
f := [seq(n*combinat[fibonacci](i), i=2..30)] ;
for sl from 0 do
for r from 1 do
if A035513(r, 1) = op(1+sl, f) then
wrks := true;
for c from 2 to 5 do
if A035513(r, c) <> op(c+sl, f) then
wrks := false;
end if;
end do:
if wrks then
print(n, f, r) ;
return r-1 ;
end if;
elif A035513(r, 1) > op(1+sl, f) then
break ;
end if;
end do:
end do:
|
|
MATHEMATICA
|
W[n_, k_] := Fibonacci[k+1] Floor[n*GoldenRatio] + (n-1) Fibonacci[k];
a[n_] := Module[{f, sl, r, c, wrks}, f = Table[n*Fibonacci[i], {i, 2, 30}]; For[sl = 0, True, sl++, For[r = 1, True, r++, Which[W[r, 1] == f[[1 + sl]], wrks = True; For[c = 2, c <= 5, c++, If[W[r, c] != f[[c+sl]], wrks = False]]; If[wrks, Return[r-1]], W[r, 1] > f[[1+sl]], Break[]]]]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|