A001463 - OEIS

%I M2438 N0965 #49 Apr 13 2022 13:25:15

%S 1,3,5,8,11,15,19,23,28,33,38,44,50,56,62,69,76,83,90,98,106,114,122,

%T 131,140,149,158,167,177,187,197,207,217,228,239,250,261,272,284,296,

%U 308,320,332,344,357,370,383,396,409,422,436,450,464,478,492,506,521,536,551,566,581,596

%N Partial sums of A001462; also a(n) is the last occurrence of n in A001462.

%C Vardi gives several identities satisfied by A001463 and this sequence.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Reinhard Zumkeller, <a href="/A001463/b001463.txt">Table of n, a(n) for n = 1..10000</a>

%H D. Marcus and N. J. Fine, <a href="http://www.jstor.org/stable/2314296">Solutions to Problem 5407</a>, Amer. Math. Monthly 74 (1967), 740-743.

%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H J. L. Rémy, <a href="http://dx.doi.org/10.1006/jnth.1997.2154">Sur la suite autodécrite de Golomb</a>, J. Number Theory, vol. 66 1997 pp. 1-28.

%H N. J. A. Sloane, <a href="/A001149/a001149.pdf">Handwritten notes on Self-Generating Sequences, 1970</a> (note that A1148 has now become A005282)

%H I. Vardi, <a href="http://dx.doi.org/10.1016/0022-314X(92)90024-J">The error term in Golomb's sequence</a>, J. Number Theory, 40 (1992), 1-11. (See also the Math. Review, 93d:11103)

%F 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

%t 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 *)

%o (Haskell)

%o a001463 n = a001463_list !! (n-1)

%o a001463_list = scanl1 (+) a001462_list

%o -- _Reinhard Zumkeller_, Apr 28 2012

%K nonn,easy,nice

%O 1,2

%A _N. J. A. Sloane_