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%I #69 Aug 11 2023 18:28:08
%S 1,1,2,3,1,5,6,7,1,1,2,11,1,13,14,15,1,1,2,3,1,5,6,23,1,1,2,27,1,29,
%T 30,31,1,1,2,3,1,5,6,7,1,1,2,11,1,13,14,47,1,1,2,3,1,5,6,55,1,1,2,59,
%U 1,61,62,63,1,1,2,3,1,5,6,7,1,1,2,11,1,13,14,15
%N a(n) is the number of locations 1..n-1 which can reach i=n-1, where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.
%C Note that location n-1 itself is counted as a term which can reach i=n-1.
%C Conjecture: a(n) is also the largest number such that starting point i=n can reach every previous location (with a(1)=1 and the same rule for jumps as in the current name).
%C A047619 appears to be the indices of 1's in this sequence.
%C A023758 appears to be the indices of terms for which a(n)=n-1.
%C A089633 appears to be the distinct values of the sequence (and its complement A158582 the missing values).
%C The sequence appears to consist of monotonically increasing runs of length 4.
%C It appears that a(A004767(n))=A100892(n) and a(A016825(n))=A100892(n)-1.
%H Kevin Ryde, <a href="/A362248/b362248.txt">Table of n, a(n) for n = 1..10000</a>
%H Kevin Ryde, <a href="/A362248/a362248.c.txt">C Code</a>
%e a(6)=5 because there are 5 starting terms from which i=5 can be reached:
%e 1, 1, 2, 3, 1
%e 1->1->2---->1
%e We can see that i=1,2,3 and trivially 5 can reach i=5. i=4 can also reach i=5:
%e 1, 1, 2, 3, 1
%e 1<-------3
%e 1->1->2---->1
%e This is a total of 5 locations, so a(6)=5.
%o (C) See links.
%Y Cf. A360746, A360745, A047619, A023758, A089633, A100892.
%K nonn
%O 1,3
%A _Neal Gersh Tolunsky_, May 12 2023
%E a(24) onwards from _Kevin Ryde_, May 17 2023
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