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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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16
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| If the initial 1 is omitted, this is 2^n mod 9. - N. J. A. Sloane (njas(AT)research.att.com).
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. - Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2004
Aside from the first term, periodic with period 6. [Charles R Greathouse IV, Nov 29 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,-1,1).
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FORMULA
| a(n) = digital root of 2^(n-1) in base 10 = 2^(n-1) (mod 9). - Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 06 2001
For n>0: a(n+6)=a(n) and a(n)=A007612(n+1)-A007612(n)=A010888(A007612(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 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 [From Paolo P. Lava (paoloplava(AT)gmail.com), Mar 04 2010]
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EXAMPLE
| 1+1+2+4+8+7+5 = 28 -> 2+8 = 10 -> a(7) = 1.
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MATHEMATICA
| a[n_] := PowerMod[2, n-1, 9]; a[0] = 1; Table[a[n], {n, 0, 104}] (* From Jean-François Alcover, Nov 29 2011 *)
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PROG
| (Other) sage: [power_mod(2, n, 9)for n in xrange(0, 105)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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
| Sequence in context: A016017 A071571 A201568 * A153130 A021406 A065075
Adjacent sequences: A029895 A029896 A029897 * A029899 A029900 A029901
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KEYWORD
| base,nonn,nice,easy
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AUTHOR
| Amela2(AT)aol.com
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EXTENSIONS
| More terms from Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2004
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