cp's OEIS Frontend

A079051 Recamán variation: a(0) = 0; for n >= 1, a(n) = a(n-1) - f(n) if that number is positive and not already in the sequence, otherwise a(n) = a(n-1) + f(n), where f(n) = floor(sqrt(n)) (A000196).

%I A079051 #26 Apr 23 2018 08:38:30
%S A079051 0,1,2,3,5,7,9,11,13,10,13,16,19,22,25,28,24,20,24,28,32,36,40,44,48,
%T A079051 43,38,33,38,43,48,53,58,63,68,73,67,61,55,49,55,61,67,73,79,85,91,97,
%U A079051 103,96,89,82,75,82,89,96,103,110,117,124,131,138,145,152,144,136,128,120
%N A079051 Recamán variation: a(0) = 0; for n >= 1, a(n) = a(n-1) - f(n) if that number is positive and not already in the sequence, otherwise a(n) = a(n-1) + f(n), where f(n) = floor(sqrt(n)) (A000196).
%D A079051 N. J. A. Sloane and Allan Wilks, On sequences of Recaman type, paper in preparation, 2006.
%H A079051 Ivan Neretin, <a href="/A079051/b079051.txt">Table of n, a(n) for n = 0..10000</a>
%H A079051 Nick Hobson, <a href="/A079051/a079051.py.txt">Python program for this sequence</a>
%F A079051 Conjecture: for n>100, 1/2 < a(n)/(n*log(n)) < 1.
%F A079051 The conjecture is false. In fact, a(n) = n^(3/2)/6 + O(n). - _N. J. A. Sloane_, Apr 29 2006
%t A079051 Fold[Append[#1, If[MemberQ[#1, (a = #1[[-1]]) - (r = Floor@Sqrt@#2)], a + r, a - r]] &, {0, 1}, Range[2, 70]] (* _Ivan Neretin_, Apr 22 2018 *)
%o A079051 (PARI) lista(nn) = {va = vector(nn+1); last = 0; for (n=1, nn, new = last - sqrtint(n); if ((new <= 0) || vecsearch(vecsort(va,,8), new), new = last + sqrtint(n)); va[n+1] = new; last = new;); va;} \\ _Michel Marcus_, Apr 23 2018
%Y A079051 Cf. A000196, A005132. Numbers missed are in A117247.
%Y A079051 Cf. A117248, A117516, A117518.
%K A079051 nonn
%O A079051 0,3
%A A079051 _Benoit Cloitre_, Feb 02 2003