login
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.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Neal Gersh Tolunsky, Jul 21 2023
EXTENSIONS
More terms from Bert Dobbelaere, Jul 23 2023
STATUS
approved