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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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If the initial 1 is omitted, this is 2^n mod 9. - N. J. A. Sloane
From Cino Hilliard, Dec 31 2004: (Start)
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)
Aside from the first term, periodic with period 6. - Charles R Greathouse IV, Nov 29 2011
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LINKS
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Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).
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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
For n > 0: a(n+6) = a(n) and a(n) = A007612(n+1) - A007612(n) = A010888(A007612(n)). - Reinhard Zumkeller, Feb 27 2006
a(n) = (1/30)*(19*(n mod 6) + 14*((n+1) mod 6) - 11*((n+2) mod 6) - ((n+3) mod 6) + 4*((n+4) mod 6) + 29*((n+5) mod 6)) - 4*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Mar 04 2010
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
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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
(PARI) a(n)=if(n, [5, 1, 2, 4, 8, 7][n%6+1], 1) \\ Charles R Greathouse IV, Nov 29 2011
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CROSSREFS
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Sequence in context: A016017 A071571 A201568 * A153130 A225746 A021406
Adjacent sequences: A029895 A029896 A029897 * A029899 A029900 A029901
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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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More terms from Cino Hilliard, Dec 31 2004
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STATUS
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approved
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