A171918 Van Eck sequence (cf. A181391) starting with a(1) = 8.

8, 0, 0, 1, 0, 2, 0, 2, 2, 1, 6, 0, 5, 0, 2, 6, 5, 4, 0, 5, 3, 0, 3, 2, 9, 0, 4, 9, 3, 6, 14, 0, 6, 3, 5, 15, 0, 5, 3, 5, 2, 17, 0, 6, 11, 0, 3, 8, 47, 0, 4, 24, 0, 3, 7, 0, 3, 3, 1, 49, 0, 5, 22, 0, 3, 7, 11, 22, 5, 7, 4, 20, 0, 9, 46, 0, 3, 12, 0, 3, 3, 1, 23, 0, 5, 16, 0, 3, 7, 19, 0, 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, ..., A171917 (same but starting with 0, 1, ..., 7).

Programs

PARI

A171918_vec(N,a=8,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 A171918gen():
    yield 8
    b, bdict = 8, {8:(1,)}
    for n in count(2):
        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,)
        yield b
A171918_list = list(islice(A171918gen(),30)) # Chai Wah Wu, Dec 21 2021

Formula

a(n+1) = A181391(n) up to the first occurrence of a(1) = 8 in A181391. - M. F. Hasler, Jun 15 2019

Extensions

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