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A020806
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Decimal expansion of 1/7.
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11
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1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2, 8, 5, 7, 1, 4, 2
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A028416(1)=7; A002371(A049084(7))=A002371(4)=6: a(n+6)=a(n), a(n+6/2)=9-a(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 06 2008]
142857 and 999999=7*142857 are first and last Kaprekar numbers with six digits. Note a(n)+a(n+3)=9. (142857^2 = 20408122449; 20408+122449 = 142857). a(n)^2 = 1, 16, 4, 64, 25, 49,... [From Paul Curtz (bpcrtz(AT)free.fr), Aug 24 2009]
The constant 19 +1/7 = 19.142857.. is the Kirchhoff index of the Moebius ladder graph on v=8 vertices. The laplacian matrix has the eigenvalues 4 (one times), 4-sqrt(2) (2 times), 4+sqrt(2) (2 times), 2 (2 times) and 0 (one times). Then the Kirchhoff index is v times the sum over the inverse, non-zero eigenvalues. - R. J. Mathar, Feb 13 2011
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REFERENCES
| H. Rademacher and O. Toeplitz, Von Zahlen und Figuren (Springer 1930, reprinted 1968), ch. 19, 'Die periodischen Dezimalbrueche'. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 06 2008]
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FORMULA
| a(n)=(1/30)*{39*(n mod 6)-[(n+1) mod 6]+24*[(n+2) mod 6]-21*[(n+3) mod 6]+19*[(n+4) mod 6]-6*[(n+5) mod 6]}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 21 2009]
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CROSSREFS
| Sequence in context: A000727 A030181 A021879 * A030210 A098798 A131783
Adjacent sequences: A020803 A020804 A020805 * A020807 A020808 A020809
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KEYWORD
| nonn,cons,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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