A232271 Start with positive integers (A000027), and at each step n >= 1 subtract from the term at position n + a(n) the value a(n).

1, 1, 2, 4, 3, 6, 7, 1, 8, 10, 11, 6, 13, 7, 15, 16, 9, 12, 30, 10, 14, 11, 23, 24, 25, 4, 27, 28, 29, -11, 31, 16, 22, 34, 21, 36, 37, 19, 39, 40, 41, 42, 43, 44, 45, 23, 47, 8, 49, 25, 51, 52, 53, 27, 34, -1, 38, 29, 59, 60, 61, 31, 63, 64, 65, 66, 67, 34, 307, 70, 71

Offset

1,3

Comments

The first 71 terms are correct if the following conjecture is true: n+a(n)<=0 or n+a(n)>71 for n >= 2^30.

The sequence of negative terms begins: -11, -1, -261, -11, -253, -319, -341, -407, -451, -528, -329, -371, -29, -31, -649, -619, -427, -737, -37, ...

Indices of negative terms: 30, 56, 330, 616, 690, 870, 930, 1110, 1230, 1288, 1410, 1590, 1624, 1736, 1770, 1820, 1830, 2010, 2072, ...

Numbers n such that a(n)=n: 1, 4, 6, 7, 10, 11, 13, 15, 16, 23, 24, 25, 27, 28, 29, 31, 34, 36, 37, 39, 40, 41, 42, 43, 44, 45, ...

The sequence of numbers n such that n+a(n)<0 begins: 1485264, 2029290, 6156150, 6872250, 8338512, 8769090, 10420410, 13448490, 16654110, 25894770, ...

Links

Table of n, a(n) for n=1..71.

Prog

(Python)
TOP = 2**30  # if enough RAM
a = [1]*TOP
for n in range(1, TOP):
  a[n]=n
for n in range(1, TOP):
  if n+a[n]<TOP and n+a[n]>0: a[n+a[n]] -= a[n]
for n in range(1, 1000):
  print(a[n], end=', ')

Crossrefs

Cf. A000027, A136119, A137319, A137417, A137418, A137894.

Sequence in context: A348915 A039819 A242424 * A194277 A226246 A216623

Adjacent sequences: A232268 A232269 A232270 * A232272 A232273 A232274

Keyword

sign

Author

Alex Ratushnyak, Nov 22 2013

Extensions

Corrected by Alex Ratushnyak, Dec 28 2013

Status

approved