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

Author

Neal Gersh Tolunsky, May 08 2023

Keywords

• nonn

Comments

This is a variant of A362746.

Examples

			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).
		

Links

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

Crossrefs

Cf. A362746.

Programs

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