A171912 Van Eck sequence (cf. A181391) starting with 2.

2, 0, 0, 1, 0, 2, 5, 0, 3, 0, 2, 5, 5, 1, 10, 0, 6, 0, 2, 8, 0, 3, 13, 0, 3, 3, 1, 13, 5, 16, 0, 7, 0, 2, 15, 0, 3, 11, 0, 3, 3, 1, 15, 8, 24, 0, 7, 15, 5, 20, 0, 5, 3, 12, 0, 4, 0, 2, 24, 14, 0, 4, 6, 46, 0, 4, 4, 1, 26, 0, 5, 19, 0, 3, 21, 0, 3, 3, 1, 11, 42, 0, 6, 20, 34, 0, 4, 20, 4

Offset: 1

Author

N. J. A. Sloane, Oct 22 2010

Keywords

• nonn

Comments

A van Eck sequence is defined recursively by a(n+1) = min { k > 0 | a(n-k) = a(n) } or 0 if this set is empty. - M. F. Hasler, Jun 12 2019

Crossrefs

Cf. A181391, A171911, ..., A171918 (same but starting with 0, 1, ..., 8).

Programs

Mathematica

t = {2};
Do[
d = Quiet[Check[Position[t, Last[t]][[-2]][[1]], 0]];
If[d == 0, x = 0, x = Length[t] - d];
AppendTo[t, x], 100]
t  (* Horst H. Manninger, Aug 30 2020 *)

PARI

A171912_vec(N, a=2, i=Map())={vector(N, n, a=if(n>1, iferr(n-mapget(i, a), E, 0)+mapput(i, a, n), a))} \\ M. F. Hasler, Jun 11 2019

Python

from itertools import count, islice
def A171912gen(): # generator of terms
    b, bdict = 2, {2:(1,)}
    for n in count(2):
        yield b
        if len(l := bdict[b]) > 1:
            b = n-1-l[-2]
        else:
            b = 0
        if b in bdict:
            bdict[b] = (bdict[b][-1],n)
        else:
            bdict[b] = (n,)
A171912_list = list(islice(A171912gen(),20)) # Chai Wah Wu, Dec 21 2021

Extensions

Name edited and cross-references added by M. F. Hasler, Jun 12 2019