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A002477
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Wonderful Demlo numbers: a(n) = ((10^n - 1)/9)^2.
(Formerly M5386 N2339)
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29
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1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 1234567900987654321, 123456790120987654321, 12345679012320987654321, 1234567901234320987654321
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| D. R. Kaprekar, On Wonderful Demlo numbers, Math. Stud., 6 (1938), 68.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..300
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Demlo Number
Eric Weisstein's World of Mathematics, Repunit
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FORMULA
| G.f.: x*(1+10*x) / ((1-x)*(1-10*x)*(1-100*x)).
a(n+1) = 100*a(n) + 20*A000042(n) + 1; a(1) = 1. [From Reinhard Zumkeller, May 31 2010]
a(n) = A000042^2.
a(n) = A075412(n)/9 = A178630(n)/18 = A178631(n)/27 = A075415(n)/36 = A178632(n)/45 = A178633(n)/54 = A178634(n)/63 = A178635(n)/72 = A059988(n)/81. [From Reinhard Zumkeller, May 31 2010]
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MAPLE
| A002477:=-(1+10*z)/(z-1)/(100*z-1)/(10*z-1); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| lst={}; Do[p=((10^n-1)/9)^2; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky, Sep 28 2008]
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PROG
| (Sage) [gaussian_binomial(n, 1, 10)^2 for n in xrange(1, 14)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]
(PARI) a(n) = (10^n\9)^2 \\ Charles R Greathouse IV, Jul 25 2011
(MAGMA) [((10^n - 1)/9)^2: n in [1..20]]; // Vincenzo Librandi, Jul 26 2011
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CROSSREFS
| Cf. A002275.
Sequence in context: A137466 A062689 A057139 * A173426 A080162 A068117
Adjacent sequences: A002474 A002475 A002476 * A002478 A002479 A002480
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Minor edits from N. J. A. Sloane (njas(AT)research.att.com), Aug 18 2009
Further edits from Reinhard Zumkeller, May 12 2010
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