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Search: id:A001463
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| A001463 |
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Partial sums of A001462; also a(n) is the last occurrence of n in A001462.
(Formerly M2438 N0965)
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+0
6
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| 1, 3, 5, 8, 11, 15, 19, 23, 28, 33, 38, 44, 50, 56, 62, 69, 76, 83, 90, 98, 106, 114, 122, 131, 140, 149, 158, 167, 177, 187, 197, 207, 217, 228, 239, 250, 261, 272, 284, 296, 308, 320, 332, 344, 357, 370, 383, 396, 409, 422, 436, 450, 464, 478, 492, 506, 521, 536, 551, 566, 581, 596
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Vardi gives several identities satisfied by A001463 and this sequence.
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.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
D. Marcus and N. J. Fine, Solutions to Problem 5407, Amer. Math. Monthly 74 (1967), 740-743.
J. L. Remy, J. Number Theory, vol. 66 1997 pp. 1-28.
I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 1-11.
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LINKS
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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.
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FORMULA
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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
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CROSSREFS
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Sequence in context: A108279 A002821 A046992 this_sequence A145197 A024169 A078126
Adjacent sequences: A001460 A001461 A001462 this_sequence A001464 A001465 A001466
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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