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

Author

Neal Gersh Tolunsky, Feb 18 2023

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

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

Programs

PARI

See Links section.

Python

def A(lastn,mode=0):
  a,n,t=[1],0,1
  while n0:
      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]])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