Search: id:A001463
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%I A001463 M2438 N0965
%S A001463 1,3,5,8,11,15,19,23,28,33,38,44,50,56,62,69,76,83,90,98,106,114,122,131,
%T A001463 140,149,158,167,177,187,197,207,217,228,239,250,261,272,284,296,308,320,
               332,
%U A001463 344,357,370,383,396,409,422,436,450,464,478,492,506,521,536,551,566,581,
               596
%N A001463 Partial sums of A001462; also a(n) is the last occurrence of n in A001462.
%C A001463 Vardi gives several identities satisfied by A001463 and this sequence.
%C A001463 The g.f. (-1+z**4+z**7-z**8+z**9-z**3-z-z**11+z**12)/(1+z)/(z**2+1)/(z-1)**3 
               conjectured by S. Plouffe in his 1992 dissertation is wrong.
%D A001463 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001463 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001463 D. Marcus and N. J. Fine, Solutions to Problem 5407, Amer. Math. Monthly 
               74 (1967), 740-743.
%D A001463 J. L. Remy, J. Number Theory, vol. 66 1997 pp. 1-28.
%D A001463 I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 
               1-11.
%H A001463 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001463 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A001463 a(n) is asymptotic to tau^(1-tau)*n^tau where tau is the golden ratio, 
               tau=(1+sqrt(5))/2. More precisely, a(n)= tau^(1-tau)*n^tau + c*n^(1/
               tau)+0(n^(1/tau)) where c is a constant around 0.6. Is there any 
               known value for c? - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 
               29 2002
%Y A001463 Sequence in context: A108279 A002821 A046992 this_sequence A145197 A024169 
               A078126
%Y A001463 Adjacent sequences: A001460 A001461 A001462 this_sequence A001464 A001465 
               A001466
%K A001463 nonn,easy,nice
%O A001463 1,2
%A A001463 N. J. A. Sloane (njas(AT)research.att.com).

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