A363193 a(1)=1, and thereafter a(n) = number of occurrences of a(k) among terms a(1..k), where k = n-a(n-1).

1, 1, 2, 2, 1, 3, 2, 1, 4, 1, 5, 3, 5, 1, 6, 5, 2, 3, 3, 4, 4, 3, 2, 5, 2, 4, 5, 5, 4, 4, 5, 5, 6, 6, 5, 7, 6, 8, 7, 2, 2, 7, 1, 7, 1, 8, 2, 2, 9, 8, 7, 8, 8, 2, 5, 5, 4, 11, 10, 3, 1, 9, 11, 5, 6, 6, 9, 1, 10, 6, 5, 3, 7, 3, 7, 2, 7, 13, 6, 8, 6, 12, 13, 13, 7, 8

Offset: 1

Author

Neal Gersh Tolunsky, May 20 2023

Keywords

• nonn
• easy

Examples

			For n=5, a(5) is the number of times a(5 - a(5-1)) = a(5 - a(4)) = a(3) = 2 has occurred in the sequence among a(1..3). It has occurred 1 time up to that point, so a(5)=1.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
• Neal Gersh Tolunsky, Scatterplot of first 30000 terms
• Neal Gersh Tolunsky, Scatterplot of first 100000 terms

Crossrefs

Cf. A354971.

Programs

Python

from bisect import bisect
from itertools import count, islice
def agen(): # generator of terms
    an, a, locs = 1, [None, 1], {1: [1]}
    yield 1
    for n in count(2):
        k = n-an
        an = bisect(locs[a[k]], k) # sum(1 for i in locs[a[k]] if i <= k)
        a.append(an)
        if an not in locs: locs[an] = []
        locs[an].append(n)
        yield an
print(list(islice(agen(), 86))) # Michael S. Branicky, May 23 2023