A362746 -id:A362746 - cp's OEIS frontend

A362890 a(1)=a(2)=1. For n>2, a(n) is the number of times that a(n-1) and a(n-2) are adjacent in the sequence thus far (in any order).

1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 2, 2, 1, 4, 1, 2, 5, 1, 1, 4, 3, 1, 3, 4, 2, 1, 6, 1, 2, 7, 1, 1, 5, 2, 2, 2, 3, 3, 1, 5, 3, 1, 6, 3, 1, 7, 2, 2, 4, 2, 3, 4, 3, 4, 5, 1, 4, 4, 1, 5, 5, 1, 6, 4, 1, 6, 5, 1, 7, 3, 1, 8, 1, 2, 8, 1, 3, 9, 1, 1, 6, 6, 1, 7, 4, 1

Offset: 1

Neal Gersh Tolunsky, May 08 2023

nonn

This is a variant of A362746.

			a(4)=2 because a(2) and a(3) = (1, 1) appear as a contiguous pair at 2 locations: at indices (1, 2) and (2, 3).
a(7)=3 because a(5) and a(6) = (1, 2) appear as a contiguous pair at 3 locations: at indices (3, 4), (4, 5), (5, 6).

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Gavin Lupo, Image of the first 100000 terms.

Cf. A362746.

from itertools import islice
from collections import Counter
def k(c, d): return (c, d) if c <= d else (d, c)
def agen(): # generator of terms
    an, anext, c = 1, 1, Counter({(1, 1)})
    while True:
        yield an
        an, anext = anext, c[k(an, anext)]
        c[k(an, anext)] += 1
print(list(islice(agen(), 100))) # Michael S. Branicky, May 09 2023

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).

Original entry on oeis.org

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

Gavin Lupo, May 18 2023

			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.

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.

Cf. A329985, A362746, A362890, A363086.

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

cp's OEIS Frontend

A362890 a(1)=a(2)=1. For n>2, a(n) is the number of times that a(n-1) and a(n-2) are adjacent in the sequence thus far (in any order).

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