A171917 Van Eck sequence (cf. A181391) starting with a(1) = 7.

7, 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, 0, 3, 3, 1, 42, 0, 5, 15, 20, 0, 4, 32, 0, 3, 11, 18, 0, 4, 7, 66, 0, 4, 4, 1, 20, 16, 0, 6, 32, 17, 36, 0, 5, 26, 0, 3, 22, 0, 3, 3, 1, 17

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 15 2019

Crossrefs

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

Programs

PARI

A171917_vec(N, a=7, 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 A171917gen(): # generator of terms
    b, bdict = 7, {7:(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,)
A171917_list = list(islice(A171917gen(),20)) # Chai Wah Wu, Dec 21 2021

Formula

a(n+1) = A181391(n) until the first occurrence of a(1) = 7 in A181391. - M. F. Hasler, Jun 15 2019

Extensions

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