

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
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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

9mod[Floor[1*Pi],9]=93=6, 9modFloor[2*Pi],9]=96=3, 9mod[Floor[3*Pi],9]=90=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}]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



