A001463 Partial sums of A001462; also a(n) is the last occurrence of n in A001462.
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
Offset: 1
References
- 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).
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- D. Marcus and N. J. Fine, Solutions to Problem 5407, Amer. Math. Monthly 74 (1967), 740-743.
- Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
- Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
- J. L. Rémy, Sur la suite autodécrite de Golomb, J. Number Theory, vol. 66 1997 pp. 1-28.
- N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282)
- I. Vardi, The error term in Golomb's sequence, J. Number Theory, 40 (1992), 1-11. (See also the Math. Review, 93d:11103)
Programs
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Haskell
a001463 n = a001463_list !! (n-1) a001463_list = scanl1 (+) a001462_list -- Reinhard Zumkeller, Apr 28 2012
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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}]] (* Harvey P. Dale, Oct 20 2011, from Robert G. Wilson v's program in A001463 *)
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, Oct 29 2002
Comments