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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. 7
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, 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, 1, 61, 62, 63, 1, 1, 2, 3, 1, 5, 6, 7, 1, 1, 2, 11, 1, 13, 14, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Note that location n-1 itself is counted as a term which can reach i=n-1.
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).
A047619 appears to be the indices of 1's in this sequence.
A023758 appears to be the indices of terms for which a(n)=n-1.
A089633 appears to be the distinct values of the sequence (and its complement A158582 the missing values).
The sequence appears to consist of monotonically increasing runs of length 4.
It appears that a(A004767(n))=A100892(n) and a(A016825(n))=A100892(n)-1.
LINKS
Kevin Ryde, C Code
EXAMPLE
a(6)=5 because there are 5 starting terms from which i=5 can be reached:
1, 1, 2, 3, 1
1->1->2---->1
We can see that i=1,2,3 and trivially 5 can reach i=5. i=4 can also reach i=5:
1, 1, 2, 3, 1
1<-------3
1->1->2---->1
This is a total of 5 locations, so a(6)=5.
PROG
(C) See links.
CROSSREFS
Sequence in context: A341635 A182938 A329445 * A055231 A304328 A304339
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, May 12 2023
EXTENSIONS
a(24) onwards from Kevin Ryde, May 17 2023
STATUS
approved

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Last modified February 29 19:20 EST 2024. Contains 370428 sequences. (Running on oeis4.)