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

1,2

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

Prog

(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

Crossrefs

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

Sequence in context: A227156 A123369 A178306 * A280153 A023671 A302243

Adjacent sequences: A309360 A309361 A309362 * A309364 A309365 A309366

Keyword

nonn

Author

Nicholas FitzGerald, Jul 25 2019

Status

approved