A137894 -id:A137894 - cp's OEIS frontend

A138095 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add: to the term at position n + 1a(n) the value 1, to the term at position n + 2a(n) the value 1, ..., to the term at position n + n*a(n) the value 1.

1, 3, 3, 4, 6, 7, 7, 10, 10, 10, 12, 14, 14, 15, 15, 17, 18, 19, 20, 23, 22, 22, 25, 24, 25, 27, 29, 30, 32, 32, 31, 32, 34, 35, 39, 36, 38, 39, 41, 42, 43, 43, 45, 46, 46, 46, 48, 52, 51, 53, 51, 52, 55, 55, 56, 59, 57, 60, 63, 62, 62, 64, 63, 65, 66, 68, 69, 70, 72, 71

Offset: 1

Ctibor O. Zizka, May 03 2008

			        n | 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20
  --------+-----------------------------------------------------------
  Step  1 |    3
  Step  2 |             6        9
  Step  3 |                7       10       13
  Step  4 |                     10          14          17          21
  Step  5 |                              12                18
  Step  6 |                                    14                   22
  Step  7 |                                       15
  Step  8 |                                                   19
  Step  9 |                                                      20
  Step 10 |                                                         23
  --------+-----------------------------------------------------------
     a(n) | 1  3  3  4  6  7  7 10 10 10 12 14 14 15 15 17 18 19 20 23

Cf. A000027, A136119, A137319, A137417, A137418, A136259, A136272, A137292, A136120, A137832, A137838, A137894, A137898, A137901, A137902, A137903.

lista(nn) = my(va = [1..nn]); for (n=1, nn, for (k=1, n, my(j = n+k*va[n]); if (j <= #va, va[j]++); )); va; \\ Michel Marcus, Aug 09 2022

Corrected and extended by Michel Marcus, Aug 09 2022

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).

Original entry on oeis.org

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

Alex Ratushnyak, Nov 22 2013

sign

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, ...

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

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=', ')

Corrected by Alex Ratushnyak, Dec 28 2013

cp's OEIS Frontend

A138095 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add: to the term at position n + 1a(n) the value 1, to the term at position n + 2a(n) the value 1, ..., to the term at position n + n*a(n) the value 1.

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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).

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cp's OEIS Frontend

A138095 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add: to the term at position n + 1*a(n) the value 1, to the term at position n + 2*a(n) the value 1, ..., to the term at position n + n*a(n) the value 1.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Extensions

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).

Views

Author

Keywords

Comments

Crossrefs

Programs

Python

Extensions

A138095 Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add: to the term at position n + 1a(n) the value 1, to the term at position n + 2a(n) the value 1, ..., to the term at position n + n*a(n) the value 1.