cp's OEIS Frontend

A362248 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.

%I A362248 #70 Dec 19 2024 11:45:36
%S A362248 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 A362248 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 A362248 1,61,62,63,1,1,2,3,1,5,6,7,1,1,2,11,1,13,14,15
%N A362248 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 A362248 Note that location n-1 itself is counted as a term which can reach i=n-1.
%C A362248 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 A362248 A047619 appears to be the indices of 1's in this sequence.
%C A362248 A023758 appears to be the indices of terms for which a(n)=n-1.
%C A362248 A089633 appears to be the distinct values of the sequence (and its complement A158582 the missing values).
%C A362248 The sequence appears to consist of monotonically increasing runs of length 4.
%C A362248 It appears that a(A004767(n))=A100892(n) and a(A016825(n))=A100892(n)-1.
%H A362248 Kevin Ryde, <a href="/A362248/b362248.txt">Table of n, a(n) for n = 1..10000</a>
%H A362248 Kevin Ryde, <a href="/A362248/a362248.c.txt">C Code</a>
%e A362248 a(6)=5 because there are 5 starting terms from which i=5 can be reached:
%e A362248   1, 1, 2, 3, 1
%e A362248   1->1->2---->1
%e A362248 We can see that i=1,2,3 and trivially 5 can reach i=5. i=4 can also reach i=5:
%e A362248   1, 1, 2, 3, 1
%e A362248   1<-------3
%e A362248   1->1->2---->1
%e A362248 This is a total of 5 locations, so a(6)=5.
%o A362248 (C) /* See links */
%Y A362248 Cf. A360746, A360745, A047619, A023758, A089633, A100892.
%K A362248 nonn
%O A362248 1,3
%A A362248 _Neal Gersh Tolunsky_, May 12 2023
%E A362248 a(24) onwards from _Kevin Ryde_, May 17 2023