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A037905 a(n) = 9 - (floor(n*Pi) mod 9). 0
6, 3, 9, 6, 3, 9, 6, 2, 8, 5, 2, 8, 5, 2, 7, 4, 1, 7, 4, 1, 7, 3, 9, 6, 3, 9, 6, 3, 8, 5, 2, 8, 5, 2, 8, 4, 1, 7, 4, 1, 7, 4, 9, 6, 3, 9, 6, 3, 9, 5, 2, 8, 5, 2, 8, 5, 1, 7, 4, 1, 7, 4, 1, 6, 3, 9, 6, 3, 9, 6, 2, 8, 5, 2, 8, 5, 2, 7, 4, 1, 7, 4, 1, 7, 3, 9, 6, 3, 9, 6, 3, 8, 5, 2, 8, 5, 2, 8, 4, 1, 7, 4, 1, 7, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A Beatty conjugate modulo 9 of the Pi irrational rotation.
What is unique about this sequence is that it can be broken up into nine "orthogonal" binary sequences. It also determines a unique irrational number that is very probably a transcendental number as well.
LINKS
FORMULA
a(n) = 9 - (floor(n*Pi) mod 9).
EXAMPLE
9-mod[Floor[1*Pi],9]=9-3=6, 9-modFloor[2*Pi],9]=9-6=3, 9-mod[Floor[3*Pi],9]=9-0=9, etc.
MATHEMATICA
f[n_] := 9 - Mod[Floor[n*\[Pi]], 9]; Table[f[n], {n, 1, 105}] (* OR *)
fn[x_, y_] := Which[9 - Mod[Floor[n*\[Pi]], 9] == y, y, True, 0]; an[y_] := N[Sum[fn[n, y]*10^(-n), {n, 1, 200}], 200]; Sum[ an[i], {i, 1, 9}]
9-Mod[Floor[Pi Range[110]], 9] (* Harvey P. Dale, Oct 24 2017 *)
CROSSREFS
Sequence in context: A093754 A135935 A263183 * A180596 A154465 A176533
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Jun 27 2002
EXTENSIONS
Edited by Robert G. Wilson v, Jun 27 2002
STATUS
approved

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Last modified May 27 01:50 EDT 2024. Contains 372847 sequences. (Running on oeis4.)