A361383 - OEIS

%I #31 Mar 20 2023 16:01:25

%S 1,1,2,3,3,4,5,4,7,7,7,7,8,8,8,8,8,8,8,15,16,15,16,15,18,17,18,19,19,

%T 19,19,19,19,19,19,19,19,19,19,22,24,22,24,23,24,26,26,26,26,26,26,26,

%U 26,26,29,32,33,35,32,35,32,35,32,35,32,35,32,36,35,37

%N a(n) is the number of locations 1..n-1 which can be reached starting from location i=a(n-1), where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.

%C For clarification: We start at the term with index a(n-1). From each term at index i, we can jump to up to two locations, which are a(i) terms away in either direction. We continue this process from the terms we have reached until we have visited all possible terms.

%H Samuel Harkness, <a href="/A361383/b361383.txt">Table of n, a(n) for n = 1..10000</a>

%e We find a(8)=4 by first looking at the previous term in the sequence so far (1,1,2,3,3,4,5), which is a(7)=5. This tells us to start at location i=5. Permitted steps can reach 4 locations as follows:

%e   1, 1, 2, 3, 3, 4, 5

%e      1<-------3

%e   1, 1, 2, 3, 3, 4, 5

%e   1<-1->2

%e Steps from each of these locations cannot reach anything new, so a(8)=4. The reachable terms are:

%e   1, 1, 2, 3, 3, 4, 5

%e   1  1  2     3

%Y Cf. A360744, A360745, A360746, A360593, A360594, A360595, A358838.

%K nonn

%O 1,3

%A _Neal Gersh Tolunsky_, Mar 09 2023

%E More terms from _Samuel Harkness_, Mar 10 2023