A171913 Van Eck sequence (cf. A181391) starting with a(1) = 3.

3, 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 20, 0, 4, 6, 9, 0, 4, 4, 1, 20, 9, 6, 8, 0, 8, 2, 22, 0, 4, 11, 0, 3, 22, 6, 12, 0, 5, 28, 0, 3, 8, 16, 0, 4, 15, 0, 3, 7, 0, 3, 3, 1, 33, 0, 5, 18, 0, 3, 7, 11, 30, 0, 5, 8, 23, 0, 4, 23, 3, 11, 10, 0, 6, 39, 0, 3, 7, 18, 22

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, i.e., a(n) does not appear earlier in the sequence. - M. F. Hasler, Jun 12 2019

Links

Table of n, a(n) for n=1..90.

Formula

a(n+1) = A181391(n) up to the first occurrence of a(1) = 3 in A181391. - M. F. Hasler, Jun 15 2019

Mathematica

t = {3};
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, Sep 08 2020 *)

Prog

(PARI) A171913_vec(N, a=3, 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 15 2019
(Python)
from itertools import count, islice
def A171913gen(): # generator of terms
    b, bdict = 3, {3:(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, )
A171913_list = list(islice(A171913gen(), 20)) # Chai Wah Wu, Dec 21 2021

Crossrefs

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

Sequence in context: A324862 A324864 A331509 * A342154 A074936 A035655

Adjacent sequences: A171910 A171911 A171912 * A171914 A171915 A171916

Keyword

nonn

Author

N. J. A. Sloane, Oct 22 2010

Extensions

Name edited and cross-references added by M. F. Hasler, Jun 15 2019

Status

approved