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

Author

Neal Gersh Tolunsky, Jul 21 2023

Keywords

• nonn
• easy

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

Examples

			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.
		

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

Crossrefs

Cf. A360593, A360746, A360745, A364882.

Programs

PARI

\\ See links.

Extensions

More terms from Bert Dobbelaere, Jul 23 2023