A137894 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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

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.