A330261 -id:A330261 - cp's OEIS frontend

A330264 Distinct values of A330261 in order of their appearance as n grows.

1, 0, -1, -2, -3, 4, -4, 5, 7, 2, -5, 3, -6, 6, -7, 9, 10, -8, 8, -14, -9, -12, 13, -16, 16, 18, 19, 15, -18, 21, -13, -17, -19, 17, -20, -25, -32, 32, -33, 33, 37, 35, -35, 39, -39, -42, 36, -38, -37, 38, 41, -34, 34, 43, -41, 12, -10, 11, 22, -21, -31, 29

Offset: 1

Rémy Sigrist, Dec 07 2019

Every integer appears in the sequence.

			The first terms of A330261 and of this sequence are:
- A330261 = 1, 0, 1, -1, 1, 0, 1, -2, 1, 1, 1, -1, 1, 0, 1, -3, 1, 4, ...
- a       = 1, 0,    -1,          -2,                       -3,    4, ...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A330264

Cf. A330261.

PARI
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See Links section.
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A330262 Start with an empty stack S; for n = 1, 2, 3, ..., interpret the binary representation of n from left to right as follows: in case of bit 1, push the number 1 on top of S, in case of bit 0, replace the two numbers on top of S, say u on top of v, with v-u; a(n) gives the number on top of S after processing n.

Original entry on oeis.org

1, 0, 1, 1, 1, 0, 1, 0, 1, -1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, -1, 1, 1, 1, 0, 1, 0, 1, -1, 1, -1, 1, 0, 1, -1, 1, -2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, -1, 1, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 0, 1, -3, 1, -3, 1, 1, 1, 0, 1, 2, 1, -2, 1

Offset: 1

Rémy Sigrist, Dec 07 2019

This sequence is a variant of A330261.
After processing n, S has A268289(n) elements.
Every integer appears infinitely many times in the sequence:
- the proof is similar to that found in A330261,
- see A330265 for the values in order of appearance.

			The first terms, alongside the binary representation of n and the evolution of stack S, are:
  n  a(n)  bin(n)  S
  -  ----  ------  ------------------------------------------------------------
  1     1       1  () -> (1)
  2     0      10  (1) -> (1,1) -> (0)
  3     1      11  (0) -> (0,1) -> (0,1,1)
  4     1     100  (0,1,1) -> (0,1,1,1) -> (0,1,0) -> (0,1)
  5     1     101  (0,1) -> (0,1,1) -> (0,0) -> (0,0,1)
  6     0     110  (0,0,1) -> (0,0,1,1) -> (0,0,1,1,1) -> (0,0,1,0)
  7     1     111  (0,0,1,0) -> (0,0,1,0,1) -> (0,0,1,0,1,1) -> (0,0,1,0,1,1,1)

Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, Scatterplot of the first 2^20 terms
Rémy Sigrist, PARI program for A330262

Cf. A268289, A308551, A330261, A330265.

PARI
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See Links section.
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cp's OEIS Frontend

A330264 Distinct values of A330261 in order of their appearance as n grows.

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