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

1,1

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

Links

Table of n, a(n) for n=1..89.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A364377 A164615 A182034 * A306605 A363929 A054876

Adjacent sequences: A171909 A171910 A171911 * A171913 A171914 A171915

Keyword

nonn

Author

N. J. A. Sloane, Oct 22 2010

Extensions

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

Status

approved