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A308551 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 by their sum; a(n) gives the number on top of S after processing n. 1
1, 2, 1, 3, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 5, 1, 12, 1, 4, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 6, 1, 15, 1, 23, 1, 2, 1, 5, 1, 4, 1, 4, 1, 2, 1, 5, 1, 4, 1, 4, 1, 2, 1, 4, 1, 3, 1, 3, 1, 2, 1, 7, 1, 19, 1, 30, 1, 2, 1, 47, 1, 57, 1, 5, 1, 2, 1, 6, 1, 20, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

After processing n, S has A268289(n) elements, the sum of which is A000788(n).

Every positive integer appears infinitely many times in the sequence.

The sequence has the same shape when represented at different scales.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Sean A. Irvine, Java program (github)

Rémy Sigrist, PARI program

Wikipedia, Stack (abstract data type)

FORMULA

a(n) = 1 iff n is odd.

a(A020989(k)) = k + 1 for any k >= 0.

If n is in A014486, then a(n) = a(n-1) + A000120(n) = 1 + A000120(n). - Charlie Neder, Jun 07 2019

EXAMPLE

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     2      10  (1) -> (1,1) -> (2)

  3     1      11  (2) -> (2,1) -> (2,1,1)

  4     3     100  (2,1,1) -> (2,1,1,1) -> (2,1,2) -> (2,3)

  5     1     101  (2,3) -> (2,3,1) -> (2,4) -> (2,4,1)

  6     2     110  (2,4,1) -> (2,4,1,1) -> (2,4,1,1,1) -> (2,4,1,2)

PROG

(Java) See Links section.

(PARI) See Links section.

CROSSREFS

Cf. A000788, A020989, A268289.

Sequence in context: A244569 A266928 A285324 * A194550 A242923 A065704

Adjacent sequences:  A308548 A308549 A308550 * A308552 A308553 A308554

KEYWORD

nonn,base,look

AUTHOR

Rémy Sigrist, Jun 07 2019

STATUS

approved

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Last modified September 15 20:41 EDT 2019. Contains 327087 sequences. (Running on oeis4.)