|
%I #39 Aug 19 2023 06:27:48
%S 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,
%T 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,
%U 5,9,6,4,9,9,5,7,6,5,5,7,5,6,6,6,7,7,9,7
%N 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.
%C 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
%H Kevin Ryde, <a href="/A364392/b364392.txt">Table of n, a(n) for n = 1..10000</a>
%H Kevin Ryde, <a href="/A364392/a364392_1.gp.txt">PARI/GP code showing periodic</a>
%H <a href="/index/Rec#order_4925">Index entries for linear recurrences with constant coefficients</a>, order 4925.
%H Neal Gersh Tolunsky, <a href="/A364392/a364392.png">Scatterplot of the ordinal transform of the first 6169 terms</a>
%e 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:
%e 1 2 3 4 5 6 7 8 9 10 11 12 location number i
%e 1,1,2,3,4,4,3,6,3, 4, 4, 6 a(i)
%e <--------------6
%e 4-------->
%e At i=10, the only jump is back to 10-a(10) = 6, which was already visited, so the path stops.
%o (PARI) See links.
%Y Cf. A360593, A360746, A360745, A364882.
%K nonn,easy
%O 1,3
%A _Neal Gersh Tolunsky_, Jul 21 2023
%E More terms from _Bert Dobbelaere_, Jul 23 2023
|
