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

1,2

Links

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

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.

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 *)

Prog

(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]<TOP: a[n+a[n]] += n
# Alex Ratushnyak, Nov 22 2013

Crossrefs

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

Sequence in context: A327726 A050066 A050064 * A087329 A298914 A205116

Adjacent sequences: A137891 A137892 A137893 * A137895 A137896 A137897

Keyword

easy,nonn

Author

Ctibor O. Zizka, Apr 30 2008

Extensions

More terms from Alex Ratushnyak, Nov 22 2013.

Status

approved