

A322510


a(1) = 0, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n)  k(n) where k(n) is the least positive integer not leading to a duplicate term in sequence a.


5



0, 1, 1, 4, 2, 2, 4, 5, 3, 6, 10, 7, 3, 8, 16, 15, 5, 12, 6, 19, 7, 9, 11, 22, 8, 9, 15, 28, 12, 14, 18, 16, 14, 10, 20, 13, 11, 17, 29, 20, 18, 21, 35, 23, 41, 24, 46, 57, 13, 26, 42, 35, 17, 25, 55, 29, 27, 30, 54, 31, 59, 32, 68
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OFFSET

1,4


COMMENTS

The point is that the same k(n) must be used for both a(2*n) and a(2*n+1).  N. J. A. Sloane, Dec 17 2019
Apparently every signed integer appears in the sequence.


LINKS

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


FORMULA

a(n) = (a(2*n) + a(2*n+1))/2.


EXAMPLE

The first terms, alongside k(n) and associate children, are:
n a(n) k(n) a(2*n) a(2*n+1)
    
1 0 1 1 1
2 1 3 4 2
3 1 3 2 4
4 4 1 5 3
5 2 8 6 10
6 2 5 7 3
7 4 12 8 16
8 5 10 15 5
9 3 9 12 6
10 6 13 19 7


PROG

(PARI) lista(nn) = my (a=[0], s=Set(0)); for (n=1, ceil(nn/2), for (k=1, oo, if (!setsearch(s, a[n]+k) && !setsearch(s, a[n]k), a=concat(a, [a[n]+k, a[n]k]); s=setunion(s, Set([a[n]+k, a[n]k])); break))); a[1..nn]


CROSSREFS

For k(n) see A330337, A330338.
See A305410, A304971 and A322574A322575 for similar sequences.
Sequence in context: A100854 A194688 A317389 * A021707 A126560 A289762
Adjacent sequences: A322507 A322508 A322509 * A322511 A322512 A322513


KEYWORD

sign,look


AUTHOR

Rémy Sigrist, Dec 13 2018


STATUS

approved



