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

1,4

Comments

This is a variant of A362746.

Links

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Gavin Lupo, Image of the first 100000 terms.

Example

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).

Prog

(Python)
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

Crossrefs

Cf. A362746.

Sequence in context: A237594 A098666 A374443 * A306251 A364027 A308967

Adjacent sequences: A362887 A362888 A362889 * A362891 A362892 A362893

Keyword

nonn

Author

Neal Gersh Tolunsky, May 08 2023

Status

approved