A363083 a(0)=a(1)=1. For n>1, if the number of occurrences of a(n-1) is less than abs(a(n-1)), then a(n)=a(n-1)-a(n-2). Otherwise, a(n)=a(n-1)+a(n-2).

1, 1, 2, 1, 3, 2, 5, 3, -2, -5, -3, 2, -1, 1, 0, 1, 1, 2, 3, 5, 2, 7, 5, -2, 3, 1, 4, 3, 7, 4, -3, -7, -4, 3, -1, 2, 1, 3, 4, 1, 5, 4, 9, 5, 14, 9, -5, -14, -9, 5, -4, -9, -5, 4, -1, 3, 2, 5, 7, 2, 9, 7, -2, 5, 3, 8, 5, 13, 8, -5, -13, -8, 5, -3, 2, -1, 1, 0

Offset

0,3

Links

Gavin Lupo, Table of n, a(n) for n = 0..50000

Gavin Lupo, Image of the first 100000 terms.

Gavin Lupo, Image of the first 1000000 terms.

Gavin Lupo, Image of the first 10000000 terms.

Gavin Lupo, Image of the first 25000000 terms.

Example

a(0) = 1
a(1) = 1
a(2) = 2. Two 1's in the list so far.    2 > abs(1).   1 + 1 = 2.
a(3) = 1. One 2 in the list so far.      1 < abs(2).   2 - 1 = 1.
a(4) = 3. Three 1's in the list so far.  3 > abs(1).   1 + 2 = 3.

Prog

(Python)
from itertools import islice
from collections import Counter
def agen(): # generator of terms
    anprev, an, c = 1, 1, Counter([1])
    yield 1
    while True:
        yield an
        c[an] += 1
        anprev, an = an, an-anprev if c[an] < abs(an) else an+anprev
print(list(islice(agen(), 80))) # Michael S. Branicky, May 18 2023

Crossrefs

Cf. A329985, A362746, A362890, A363086.

Sequence in context: A050360 A175003 A176431 * A348112 A045747 A308984

Adjacent sequences: A363080 A363081 A363082 * A363084 A363085 A363086

Keyword

sign,easy,look

Author

Gavin Lupo, May 18 2023

Status

approved