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A029898
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Pitoun's sequence: a(n+1) is digital root of a(0) + ... + a(n).
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18
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1, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, 5, 1, 2
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OFFSET
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0,3
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COMMENTS
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Except for the initial term, also the digital root of 11^n.
Except for the initial term, also the decimal expansion of 125/1001.
Except for the initial term, also the digital root of 2^n. (End)
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LINKS
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FORMULA
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a(n) = digital root of 2^(n-1) in base 10 = 2^(n-1) (mod 9). - Olivier Gérard, Jun 06 2001
a(n) = (9 + cos(n*Pi) - 4*sqrt(3)*sin(n*Pi/3))/2 for n > 0 with a(0)=1. - Wesley Ivan Hurt, Oct 04 2018
O.g.f.: (1 + x^2 + 3*x^3 + 4*x^4)/((1 - x)*(1 + x)*(1 - x + x^2)).
E.g.f.: 5*cosh(x) - 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) + 4*(sinh(x) - 1). (End)
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EXAMPLE
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1 + 1 + 2 + 4 + 8 + 7 + 5 = 28 -> 2 + 8 = 10 -> a(7) = 1.
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MATHEMATICA
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a[n_] := PowerMod[2, n-1, 9]; a[0] = 1; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Nov 29 2011 *)
Join[{1}, LinearRecurrence[{1, 0, -1, 1}, {1, 2, 4, 8}, 110]] (* or *) Join[{1}, PowerMod[2, Range[110], 9]] (* Harvey P. Dale, Nov 24 2014 *)
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PROG
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(Sage) [power_mod(2, n, 9)for n in range(0, 105)] # Zerinvary Lajos, Nov 03 2009
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CROSSREFS
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KEYWORD
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base,nonn,nice,easy
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AUTHOR
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Amela2(AT)aol.com
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EXTENSIONS
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STATUS
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approved
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