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A100402
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Digital root of 4^n.
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9
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1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7, 1, 4, 7
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OFFSET
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0,2
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COMMENTS
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Digital root of the powers of any number congruent to 4 mod 9. - Alonso del Arte, Jan 26 2014
The period 3 digits of this sequence are the same as those of A070403 (digital root of 7^n) but the order is different: [1, 4, 7] vs. [1, 7, 4].
The digits in this sequence appear in the decimal expansions of the following rational numbers: 49/333, 490/333, 4900/333, .... (End)
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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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a(n) = a(n-3) for n>2.
G.f.: (1+4*x+7*x^2)/ ((1-x)*(1+x+x^2)). (End)
a(n) = 4 - 3*cos(2*n*Pi/3) - sqrt(3)*sin(2*n*Pi/3). - Wesley Ivan Hurt, Jun 30 2016
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EXAMPLE
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4^2 = 16, digitalroot(16) = 7, the third entry.
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MATHEMATICA
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PROG
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(Sage) [power_mod(4, n, 9) for n in range(0, 105)] # Zerinvary Lajos, Nov 25 2009
(PARI) a(n)=[1, 4, 7][1+n%3]; \\ Joerg Arndt, Aug 26 2014
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CROSSREFS
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Cf. A000302, A1001022, A009966, A009975, A009984, A010872, A010888, A070403, A087752, A121013, A141725, A016777.
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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