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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.
2
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
1,20
COMMENTS
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.
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 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)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Dec 07 2019
STATUS
approved