A309363 Van Eck's sequence (cf. A181391), but outputting 2 for a new number, not 0.

0, 2, 2, 1, 2, 2, 1, 3, 2, 3, 2, 2, 1, 6, 2, 3, 6, 3, 2, 4, 2, 2, 1, 10, 2, 3, 8, 2, 3, 3, 1, 8, 5, 2, 6, 18, 2, 3, 8, 7, 2, 4, 22, 2, 3, 7, 6, 12, 2, 5, 17, 2, 3, 8, 15, 2, 4, 15, 3, 6, 13, 2, 6, 3, 5, 15, 8, 13, 7, 23, 2, 9, 2, 2, 1, 44

Offset: 1

Author

Nicholas FitzGerald, Jul 25 2019

Keywords

• nonn

Comments

After the initial value, the sequence is extended by a(n+1) = min { k > 0: a(n-k) = a(n) } or 2 if no such k exists, i.e., if a(n) did not appear earlier.

Although the sequence has properties that are superficially similar to the original A181391, there is an important difference. Using a positive number m instead of 0 to mark a new value means there is no 1-to-1 correspondence between the occurrence of a new value and the occurrence of m. - Jan Ritsema van Eck, Aug 14 2019

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A181391, A171911, ..., A171918 (same but starting with 0, 1, 2, ..., 8 and returning 0 when a new term appears).

Programs

Python

from itertools import count, islice
def A309363gen(): # generator of terms
    b, bdict = 0, {0:(1,)}
    for n in count(2):
        yield b
        if len(l := bdict[b]) > 1:
            b = n-1-l[-2]
        else:
            b = 2
        if b in bdict:
            bdict[b] = (bdict[b][-1],n)
        else:
            bdict[b] = (n,)
A309363_list = list(islice(A309363gen(),20)) # Chai Wah Wu, Dec 21 2021