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

Author

Alex Ratushnyak, Nov 22 2013

Keywords

• sign

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, ...

Crossrefs

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

Programs

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]0: a[n+a[n]] -= a[n]
for n in range(1,1000):
  print(a[n], end=', ')

Extensions

Corrected by Alex Ratushnyak, Dec 28 2013