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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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.
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).
I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 1-11.
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LINKS
| 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
| 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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MATHEMATICA
| Accumulate[a[1]=1; a[n_]:=a[n]=1+a[n-a[a[n-1]]]; Table[a[n], {n, 84}]] (* From Harvey P. Dale, Oct 20 2011, from Robert G. Wilson's program in A001463 *)
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CROSSREFS
| Sequence in context: A108279 A002821 A046992 * A145197 A024169 A078126
Adjacent sequences: A001460 A001461 A001462 * A001464 A001465 A001466
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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