A359007 a(n) = b(n-b(n)) where b is Van Eck's sequence A181391.

0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 5, 1, 0, 0, 0, 2, 4, 0, 5, 0, 6, 0, 3, 0, 0, 2, 5, 0, 4, 14, 6, 3, 0, 6, 15, 5, 3, 9, 0, 5, 3, 0, 6, 5, 0, 3, 8, 3, 6, 0, 3, 2, 0, 0, 5, 9, 0, 4, 1, 0, 0, 3, 32, 0, 4, 11, 0, 7, 17, 0, 3, 11, 0, 2, 31, 6, 31, 0, 0, 6, 3, 0, 9, 2, 33, 3, 0, 3, 15, 0, 5

Offset

1,7

Comments

In Van Eck's sequence, b(n) is the distance between b(n-1) and the previous occurrence of b(n-1) there. Taking a(n) = b(n-b(n)) is therefore the distance between the second and third last occurrence of b(n-1) there.

If b(n-1) has not yet occurred three times then the result is a(n) = 0 either by b(n)=0 when b(n-1) has only occurred once, or b(n-b(n)) = 0 when b(n-1) has only occurred twice.

Links

Table of n, a(n) for n=1..94.

Example

b(14) is 2, so we count back two steps to b(12), which is 5. Therefore a(14) = 5. As b(14-1) = b(13) = 0, the three occurrences of 0's are separated by b(14) and b(12) = a(14), that is, 2 and 5 steps:
.
         n: ...  5   6   7   8   9  10  11  12  13  14  15  16  ...
.
                     |<--------5-------->|<--2-->|
                     |                   |       |
                     |                   |       |
      b(n): ...  2,  0,  2,  2,  1,  6,  0,  5,  0,  2,  6,  5, ...
                                             |       |
                                             v       |
                                     a(14) = 5 <-----
                                              two steps
                                                back

Prog

(PARI) A181391_vec(N, a=0, i=Map())={vector(N, n, a=if(n>1, iferr(n-mapget(i, a), E, 0)+mapput(i, a, n)))};
lista(nn) = my(v = A181391_vec(nn)); vector(#v, k, v[k-v[k]]); \\ Michel Marcus, Dec 11 2022

Crossrefs

Cf. A181391.

Sequence in context: A340683 A221645 A216176 * A128765 A193511 A254218

Adjacent sequences: A359004 A359005 A359006 * A359008 A359009 A359010

Keyword

nonn,easy

Author

Tamas Sandor Nagy, Dec 10 2022

Status

approved