login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A360744 a(n) is the maximum number of locations 1..n-1 which can be reached starting from some location s, where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example. 10
1, 1, 2, 3, 4, 5, 5, 6, 6, 7, 7, 9, 10, 10, 10, 11, 11, 13, 14, 14, 14, 15, 15, 15, 15, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 26, 27, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 32, 32, 32, 32, 33, 33, 35, 35, 41, 42, 42, 42, 43, 43, 43, 44, 44, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 49, 49, 51, 51, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
a(10)=7 is the earliest term whose solution cannot be represented by a single path in which each index is visited once.
LINKS
EXAMPLE
For a(9), we reach the greatest number of terms by starting at location s=4, which is a(4)=3. We visit 6 terms as follows (each line shows the next unvisited term(s) we can reach from the term(s) last visited):
1, 1, 2, 3, 4, 5, 5, 6
1<-------3------->5
1, 1, 2, 3, 4, 5, 5, 6
1->1<-------------5
1, 1, 2, 3, 4, 5, 5, 6
1->2
1, 1, 2, 3, 4, 5, 5, 6
2---->4
From the last iteration we can visit no new terms. We reached 6 terms, so a(9)=6:
1, 1, 2, 3, 4, 5, 5, 6
1 1 2 3 4 5
PROG
(Python)
def A(lastn, mode=0):
a, n, t=[1], 0, 1
while n<lastn:
p, v=0, 1
while p<=n:
d, g, r, rr=[[p]], 0, 0, [p]
while len(d)>0:
if not d[-1][-1] in rr:rr.append(d[-1][-1])
if d[-1][-1]-a[d[-1][-1]]>=0:
if d[-1].count(d[-1][-1]-a[d[-1][-1]])<t:g=1
if d[-1][-1]+a[d[-1][-1]]<=n:
if d[-1].count(d[-1][-1]+a[d[-1][-1]])<t:
if g>0: d.append(d[-1][:])
d[-1].append(d[-1][-1]+a[d[-1][-1]])
r=1
if g>0:
if r>0: d[-2].append(d[-2][-1]-a[d[-2][-1]])
else: d[-1].append(d[-1][-1]-a[d[-1][-1]])
r=1
if r==0:d.pop()
r, g=0, 0
if v<len(rr):v=len(rr)
p+=1
a.append(v)
n+=1
print(n+1, a[n])
if mode>0: print(a)
return a ## S. Brunner, Feb 19 2023
CROSSREFS
Sequence in context: A365339 A046108 A079411 * A198454 A063882 A097873
KEYWORD
nonn
AUTHOR
Neal Gersh Tolunsky, Feb 18 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 19:46 EDT 2024. Contains 373532 sequences. (Running on oeis4.)