A360746 a(n) is the maximum number of locations 1..n-1 which can be reached starting from a(n-1), where jumps from location i to i +- a(i) are permitted (within 1..n-1); a(1)=1. See example.

1, 1, 2, 3, 4, 4, 5, 5, 5, 7, 8, 8, 8, 9, 9, 12, 10, 10, 12, 10, 12, 13, 13, 13, 16, 14, 14, 16, 17, 17, 17, 18, 18, 24, 25, 25, 25, 26, 27, 27, 27, 27, 28, 28, 30, 28, 33, 28, 29, 30, 30, 30, 33, 31, 31, 31, 32, 32, 33, 33, 31, 31, 32, 33, 33, 35, 33, 37

Offset

1,3

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Example

a(7)=5 because we reach 5 terms starting from the most recent term a(6) (each line shows the next unvisited term(s) we can reach from the term(s) in the previous iteration):
1, 1, 2, 3, 4, 4
   1<----------4
1, 1, 2, 3, 4, 4
1<-1->2
1, 1, 2, 3, 4, 4
      2---->4
From the last iteration we can visit no new terms. We reached 5 terms, so a(7)=5:
1, 1, 2, 3, 4, 4
1  1  2     4  4

Prog

(Python)
def A(lastn, mode=0):
  a, n, t=[1], 0, 1
  while n<lastn:
    d, g, r, rr=[[n]], 0, 0, [n]
    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
    a.append(len(rr))
    n+=1
    print(n+1, a[n])
    if mode>0: print(a)
  return a  # S. Brunner, Feb 26 2023
(PARI) See Links section.

Crossrefs

Cf. A360744, A360745, A360593, A360594, A360595, A359005, A358838, A359008.

Sequence in context: A172006 A172005 A200247 * A056791 A333262 A218767

Adjacent sequences: A360743 A360744 A360745 * A360747 A360748 A360749

Keyword

nonn

Author

Neal Gersh Tolunsky, Feb 18 2023

Status

approved