OFFSET
1,8
COMMENTS
This sequence is a variant of A308551.
After processing n, S has A268289(n) elements.
Every integer appears infinitely many times in the sequence:
- the effect of the binary string b(0) = "110" is to leave 0 on top of S,
- the effect of the binary string b(1) = "1" is to leave 1 on top of S,
- the effect of the binary string b(-1) = "11100" is to leave -1 on top of S,
- let "|" denote the binary concatenation,
- for any k > 0:
- the effect of b(k+1) = b(-1)|b(k)|"0" is to leave k+1 on top of S,
- the effect of b(-k-1) = b(1)|b(-k)|"0" is to leave -k-1 on top of S,
- for any k, for any n > 0, if the binary representation of n ends with b(k), then a(n) = k, QED,
- see A330264 for the values in order of appearance.
LINKS
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 A330261
FORMULA
a(2*k-1) = 1 for any k > 0.
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) -> (0,2) -> (0,2,1)
6 0 110 (0,2,1) -> (0,2,1,1) -> (0,2,1,1,1) -> (0,2,1,0)
7 1 111 (0,2,1,0) -> (0,2,1,0,1) -> (0,2,1,0,1,1) -> (0,2,1,0,1,1,1)
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Dec 07 2019
STATUS
approved