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A082784
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Characteristic function of multiples of 7.
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14
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1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(0)=1, a(n)=0 for 1<=n<7, a(n+7)=a(n).
a(n)=1-A109720(n); a(A008589(n))=1; a(A047304(n))=0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
This sequence is the Euler transformation of A185017.- Jason Kimberley, Oct 14 2011
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LINKS
| Index entries for characteristic functions
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FORMULA
| a(n) = 0^(n mod 7).
a(n)=(1/147)*[ -20*(n mod 7)+((n+1) mod 7)+((n+2) mod 7)+((n+3) mod 7)+((n+4) mod 7)+((n+5) mod 7)+22*((n+6) mod 7)] - Paolo P. Lava (paoloplava(AT)gmail.com), Sep 29 2006
a(n)=-1*((n^6 mod 7)-1) - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 02 2006
Multiplicative with a(p) = (if p=7 then 1 else 0), p prime. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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EXAMPLE
| a(14)=a(2*7)=1; a(41)=a(5*7+6)=0.
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CROSSREFS
| Cf. A008589, A076309.
Characteristic function of multiples of g: A000007 (g=0), A000012 (g=1), A059841 (g=2), A079978 (g=3), A121262 (g=4), A079998 (g=5), A079979 (g=6), this sequence (g=7). - Jason Kimberley, Oct 14 2011
Sequence in context: A015283 A014548 A015087 * A058342 A014045 A015269
Adjacent sequences: A082781 A082782 A082783 * A082785 A082786 A082787
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KEYWORD
| nonn,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 22 2003
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