A137894 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 n.

1, 3, 3, 4, 7, 9, 7, 12, 9, 10, 11, 17, 13, 21, 21, 16, 17, 27, 19, 38, 21, 33, 23, 24, 25, 39, 27, 28, 41, 30, 31, 48, 33, 51, 49, 51, 37, 57, 39, 40, 41, 63, 43, 44, 63, 69, 47, 72, 49, 75, 51, 52, 53, 81, 77, 84, 57, 78, 59, 90, 61, 93, 63, 64, 91, 99, 67, 68, 69, 99

Offset: 1

Author

Ctibor O. Zizka, Apr 30 2008

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272.

Programs

Maple

mx:= 10000: # maximal index needed
b:= proc(n) n end:
a:= proc(n) option remember; global mx; local h, t;
      if n=0 then 0 else a(n-1); t:= b(n);
        if n+t<=mx then h:=b(t+n); b(t+n):=h+n fi; t
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 04 2015

Mathematica

mx = 10000 (* maximal index needed *); b[n_] := n; a[n_] := a[n] = Module[{h, t}, If[n == 0, 0, a[n-1]; t = b[n]; If[n+t <= mx, h = b[t+n]; b[t+n] = h+n]; t]]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 24 2016, after Alois P. Heinz *)

Python

TOP = 1000
a = [1]*TOP
for n in range(1,TOP):
  a[n]=n
for n in range(1,TOP):
  print(str(a[n]),end=',')
  if n+a[n]Alex Ratushnyak, Nov 22 2013

Formula

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 n.

Extensions

More terms from Alex Ratushnyak, Nov 22 2013.