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A056992
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Digital roots of square numbers A000290.
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6
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1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9, 4, 1, 9, 1, 4, 9, 7, 7, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is also the decimal expansion of 499264730/333333333 [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Jul 28 2009]
a(n) is also the digital root of Demlo numbers (A002477) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 20 2009]
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n)=1+9*{(n^2-1)/9} , where the symbol {} means fractional part. [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 20 2009]
Cyclic with a period of nine. Note that (7, 9, 4, 1, 9, 1, 4, 9, 7) is palindromic.
a(n)=(1/108)*{113*(n mod 9)-79*[(n+1) mod 9]+53*[(n+2) mod 9]+77*[(n+3) mod 9]-7*[(n+4) mod 9]+17*[(n+5) mod 9]+41*[(n+6) mod 9]-43*[(n+7) mod 9]-19*[(n+8) mod 9]}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Aug 04 2009]
a(n)=3(1+cos(2n*pi/3)+ cos(4n*pi/3))+mod(3n^4+3n^6+4n^8,9) [From Ant King (mathstutoring(AT)ntlworld.com), Oct 07 2009]
GF: x (1+4x+9x^2+7x^3+7x^4+9x^5+4x^6+x^7+9x^8)/((1-x)(1+x+x^2)(1+x^3+x^6)) [From Ant King (mathstutoring(AT)ntlworld.com), Oct 20 2009]
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MATHEMATICA
| DigitalRoot[n_Integer?NonNegative] := 1 + 9*FractionalPart[(n - 1)/9] A056992[n_]:=DigitalRoot[n^2] [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Dec 20 2009]
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CROSSREFS
| Cf. A000290, A056991.
Sequence in context: A018880 A166923 A021205 * A169908 A004159 A092554
Adjacent sequences: A056989 A056990 A056991 * A056993 A056994 A056995
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KEYWORD
| nonn,base,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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