A364392 a(1)=1 and thereafter a(n) is the least number of locations 1..n-1 which can be visited in a single path beginning at i=n-1, in which one proceeds from location i to i +- a(i) (within 1..n-1) until no further unvisited location is available.

1, 1, 2, 3, 4, 4, 3, 6, 3, 4, 4, 6, 3, 5, 4, 7, 5, 5, 6, 6, 5, 6, 6, 6, 6, 7, 3, 8, 5, 8, 7, 5, 6, 6, 7, 7, 9, 5, 9, 7, 5, 8, 7, 8, 3, 6, 9, 9, 7, 6, 4, 6, 6, 6, 10, 7, 7, 5, 10, 3, 6, 7, 7, 8, 3, 8, 6, 5, 9, 6, 4, 9, 9, 5, 7, 6, 5, 5, 7, 5, 6, 6, 6, 7, 7, 9, 7

Offset

1,3

Comments

The sequence is 1244 initial terms followed by a repeating block of 4925 terms so that a(n) = a(n-4925) for n >= 6170. - Kevin Ryde, Jul 31 2023

Links

Kevin Ryde, Table of n, a(n) for n = 1..10000

Kevin Ryde, PARI/GP code showing periodic

Index entries for linear recurrences with constant coefficients, order 4925.

Neal Gersh Tolunsky, Scatterplot of the ordinal transform of the first 6169 terms

Example

a(13)=3 because beginning at the most recent location i=n-1=12, where a(12)=6, we can visit (the fewest possible) 3 locations in a single path as follows:
  1 2 3 4 5 6 7 8 9 10 11 12   location number i
  1,1,2,3,4,4,3,6,3, 4, 4, 6   a(i)
            <--------------6
            4-------->
At i=10, the only jump is back to 10-a(10) = 6, which was already visited, so the path stops.

Prog

(PARI) See links.

Crossrefs

Cf. A360593, A360746, A360745, A364882.

Sequence in context: A286549 A286551 A290097 * A366681 A241283 A274095

Adjacent sequences: A364389 A364390 A364391 * A364393 A364394 A364395

Keyword

nonn,easy

Author

Neal Gersh Tolunsky, Jul 21 2023

Extensions

More terms from Bert Dobbelaere, Jul 23 2023

Status

approved