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A153130
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Period 6: repeat [1, 2, 4, 8, 7, 5].
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27
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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).
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
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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FORMULA
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G.f.: (1+x+2x^2+5x^3)/((1-x)(1+x)(1-x+x^2)). - R. J. Mathar, Jan 23 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) = 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)
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MAPLE
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MATHEMATICA
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Flatten[Table[{1, 2, 4, 8, 7, 5}, {20}]] (* Paul Curtz, Dec 19 2008 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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