A137417 - OEIS

%I #20 Feb 18 2024 08:27:18

%S 1,3,3,4,8,9,7,12,9,10,11,12,21,21,24,16,17,27,19,42,21,33,23,36,25,

%T 26,27,28,29,30,31,48,33,72,56,36,37,57,63,40,41,63,43,44,72,69,47,48,

%U 49,75,51,78,53,81,88,84,57,87,59,126,61,135,63,64,65,99,67,68,69,70,71

%N Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value a(n).

%C At the vast majority of positions the term is changed at most once, but at some positions a change occurs twice. An example is position 20. In step 4 the term at position 4 + a(4) = 8 is changed to 8 + a(4) = 12; in step 8 the term at position 8 + a(8) = 20 is changed to 20 + a(8) = 32; in step 10 the term at position 10 + a(10) = 20 is changed to a(20) + a(10) = 32 + 10 = 42.

%C The first position where the term is changed three times is 3498. [_Klaus Brockhaus_, Apr 23 2008]

%C The first position where the term is changed four times is 1024914. [_Rémy Sigrist_, Mar 11 2017]

%H Rémy Sigrist, <a href="/A137417/b137417.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A137417/a137417.png">Scatterplot of first 2000000 terms</a>

%t Block[{a, nn = 71}, a = Range[Max[3, IntegerLength[nn]] nn]; Do[a[[n + a[[n]]]] = a[[n + a[[n]]]] + a[[n]], {n, nn}]; a[[1 ;; nn]] ] (* _Michael De Vlieger_, Jul 28 2021 *)

%Y Cf. A000027.

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, Apr 16 2008

%E Extended by _Klaus Brockhaus_, Apr 23 2008