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A153130
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Period 6: repeat [1, 2, 4, 8, 7, 5].
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26
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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, 4, 8, 7, 5
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OFFSET
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0,2
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COMMENTS
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Digital root of 2^n.
A regular version of Pitoun's sequence: a(n) = A029898(n+1).
Also obtained from permutations of A141425, A020806, A070366, A153110, A153990, A154127, A154687, or A154815.
This sequence and its (again period 6) repeated differences produce the table:
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, -1, -2, -4, 1, 2, 4, -1, -2, ...
1, 2, -5, -1, -2, 5, 1, 2, -5, -1, -2, ...
1, -7, 4, -1, 7, -4, 1, -7, 4, -1, 7, ...
-8, 11, -5, 8,-11, 5, -8, 11, -5, 8,-11, ...
19,-16, 13,-19, 16,-13, 19,-16, 13,-19, 16, ...
-35, 29,-32, 35,-29, 32,-35, 29,-32, 35,-29, ...
64,-61, 67,-64, 61,-67, 64,-61, 67,-64, 61, ...
If each entry of this table is read modulo 9 we obtain the very regular table:
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
1, 2, 4, 8, 7, 5, 1, 2, 4, 8, 7, ...
Also the decimal expansion of the constant 125/1001. - R. J. Mathar, Jan 23 2009
Terms of the simple continued fraction of 254/(sqrt(548587) - 565). - Paolo P. Lava, Feb 17 2009
Digital root of the powers of any number congruent to 2 mod 9. - Alonso del Arte, Jan 26 2014
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REFERENCES
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Cecil Balmond, Number 9: The Search for the Sigma Code. Munich, New York: Prestel (1998): 203.
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LINKS
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Table of n, a(n) for n=0..107.
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).
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FORMULA
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a(n) = (1/30) * (29*(n mod 6) + 19 * ((n+1) mod 6) + 14 * ((n+2) mod 6) - 11 * ((n+3) mod 6) - ((n+4) mod 6) + 4 * ((n+5) mod 6). - Paolo P. Lava, Dec 19 2008
a(n) + a(n+3) = 9 = A010734(n).
G.f.: (1+x+2x^2+5x^3)/((1-x)(1+x)(1-x+x^2)). - R. J. Mathar, Jan 23 2009
a(n) = A082365(n) mod 9. - Paul Curtz, Mar 31 2009
a(n) = -1/2*cos(Pi*n) - 3*cos(1/3*Pi*n) - 3^(1/2)*sin(1/3*Pi*n) + 9/2. - Leonid Bedratyuk, May 13 2012
a(n) = A010888(A004000(n+1)). - Ivan N. Ianakiev, Nov 27 2014
From Wesley Ivan Hurt, Apr 20 2015: (Start)
a(n) = a(n-6) for n>5.
a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
a(n) = (2+3*(n-1 mod 3))*(n mod 2) + (1+3*(-n mod 3))*(n-1 mod 2). (End)
a(n) = 2^n mod 9. - Nikita Sadkov, Oct 06 2018
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MAPLE
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seq(op([1, 2, 4, 8, 7, 5]), n=0..40); # Wesley Ivan Hurt, Jul 05 2016
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MATHEMATICA
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Flatten[Table[{1, 2, 4, 8, 7, 5}, {20}]] (* Paul Curtz, Dec 19 2008 *)
Table[Mod[2^n, 9], {n, 0, 99}] (* Alonso del Arte, Jan 26 2014 *)
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PROG
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(PARI) a(n)=lift(Mod(2, 9)^n) \\ Charles R Greathouse IV, Apr 21 2015
(MAGMA) &cat [[1, 2, 4, 8, 7, 5]^^30]; // Wesley Ivan Hurt, Jul 05 2016
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CROSSREFS
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Cf. A030132, A145389, A189510.
Cf. digital roots of powers of c mod 9: c = 4, A100402; c = 5, A070366; c = 7, A070403; c = 8, A010689.
Sequence in context: A071571 A201568 A029898 * A225746 A021406 A065075
Adjacent sequences: A153127 A153128 A153129 * A153131 A153132 A153133
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Dec 19 2008
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EXTENSIONS
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Edited by R. J. Mathar, Apr 09 2009
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STATUS
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approved
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