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A255671
Number of the column of the Wythoff array (A035513) that contains U(n), where U = A001950, the upper Wythoff sequence.
3
2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 8, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 10, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 8, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 8, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4, 2, 2, 6, 2, 4, 2, 2, 4
OFFSET
1,1
COMMENTS
All the terms are even, and every even positive integer occurs infinitely many times.
FORMULA
a(n) = 2 if and only if n = L(j) for some j; otherwise, n = U(k) for some k.
a(n) = A255670(n) + 1 = A035612(A001950(n)).
EXAMPLE
Corner of the Wythoff array:
1 2 3 5 8 13
4 7 11 18 29 47
6 10 16 26 42 68
9 15 24 39 63 102
L = (1,3,4,6,8,9,11,...); U = (2,5,7,10,13,15,18,...), so that
A255670 = (1,3,1,1,5,...) and A255671 = (2,4,2,2,6,...).
MATHEMATICA
z = 13; r = GoldenRatio; f[1] = {1}; f[2] = {1, 2};
f[n_] := f[n] = Join[f[n - 1], Most[f[n - 2]], {n}]; f[z];
g[n_] := g[n] = f[z][[n]]; Table[g[n], {n, 1, 100}] (* A035612 *)
Table[g[Floor[n*r]], {n, 1, (1/r) Length[f[z]]}] (* A255670 *)
Table[g[Floor[n*r^2]], {n, 1, (1/r^2) Length[f[z]]}] (* A255671 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 03 2015
STATUS
approved