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

Author

N. J. A. Sloane, Oct 22 2010

Keywords

• nonn

Comments

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.

Links

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

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Python

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

Extensions

Edited by M. F. Hasler, Jun 11 2019