A171917 -id:A171917 - cp's OEIS frontend

A171911 Van Eck's sequence (cf. A181391), but starting with a(1) = 1.

1, 0, 0, 1, 3, 0, 3, 2, 0, 3, 3, 1, 8, 0, 5, 0, 2, 9, 0, 3, 9, 3, 2, 6, 0, 6, 2, 4, 0, 4, 2, 4, 2, 2, 1, 23, 0, 8, 25, 0, 3, 19, 0, 3, 3, 1, 11, 0, 5, 34, 0, 3, 7, 0, 3, 3, 1, 11, 11, 1, 3, 5, 13, 0, 10, 0, 2, 33, 0, 3, 9, 50, 0, 4, 42, 0, 3, 7, 25, 40, 0, 5, 20, 0, 3, 8, 48, 0, 4, 15

Offset: 1

N. J. A. Sloane, Oct 22 2010

nonn

After the initial value, the sequence is extended by a(n+1) = min { k > 0: a(n-k) = a(n) } or 0 if no such k exists, i.e., if a(n) did not appear earlier.

Chai Wah Wu, Table of n, a(n) for n = 1..10001

Cf. A181391, A171912, A171913, A171914, A171915, A171916, A171917, A171918 (same but starting with 0, 2, ..., 8).

t = {1};
Do[
d = Quiet[Check[Position[t, Last[t]][[-2]][[1]], 0], Part::partw];
If[d == 0, x = 0, x = Length[t] - d];
AppendTo[t, x], 100]
t (* Horst H. Manninger, Aug 03 2020 *)

A171911_vec(N,a=1,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

A171911_list, l = [1, 0], 0
for n in range(1, 10**4):
    for m in range(n-1, -1, -1):
        if A171911_list[m] == l:
            l = n-m
            break
    else:   # break did not occur
        l = 0
    A171911_list.append(l) # Chai Wah Wu, Jan 02 2015

Edited by M. F. Hasler, Jun 11 2019

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

Original entry on oeis.org

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

N. J. A. Sloane, Oct 22 2010

nonn

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

Cf. A181391, A171911, ..., A171917 (same but starting with 0, 1, ..., 7).

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

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

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

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

cp's OEIS Frontend

A171911 Van Eck's sequence (cf. A181391), but starting with a(1) = 1.

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