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Search: id:A001019
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| A001019 |
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Powers of 9.
(Formerly M4653 N1992)
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+0
32
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| 1, 9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Same as Pisot sequences E(1,9), L(1,9), P(1,9), T(1,9). See A008776 for definitions of Pisot sequences.
Except for 1, the largest n-th power with n digits. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Feb 09 2002
The 2002 comment by Amarnath Murthy should say more precisely "n-th power with *at most* n digits": a(22) has only 21 digits etc., a(44) has only 42 digits etc. [From Hagen von Eitzen (math(AT)von-eitzen.de), May 17 2009]
A000005(a(n)) = A005408(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
With a different offset, number of n-permutations (n>=0) of 10 objects: q, r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly zero (0) or free u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
1/1 + 1/9 + 1/81 + ... = 9/8 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2008]
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n=0..100
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 274
Tanya Khovanova, Recursive Sequences
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(n) = 9^n; a(n) = 9a(n-1).
G.f.: 1/(1-9x), e.g.f.: exp(9x)
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MAPLE
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with(finance):seq(futurevalue(1, 8, n), n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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PROGRAM
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sage: from sage.combinat.sloane_functions import recur_gen2b sage: it =recur_gen2b(1, n/6, n/6, 0, lambda n: 0) sage: [it.next() for i in range(18)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
(Other) sage: [lucas_number1(n, 9, 0) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Cf. A067470.
Sequence in context: A120997 A125630 A100062 this_sequence A074118 A050739 A158779
Adjacent sequences: A001016 A001017 A001018 this_sequence A001020 A001021 A001022
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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