A339310 a(n) = a(n-1-a(n-1)) + a(n-a(n-2)) for n>2; starting with a(1) = a(2) = 1.

1, 1, 2, 3, 3, 3, 5, 4, 6, 5, 6, 8, 8, 6, 9, 8, 8, 11, 11, 10, 10, 14, 12, 11, 16, 15, 12, 17, 14, 17, 16, 18, 14, 19, 19, 16, 21, 22, 19, 21, 25, 18, 22, 25, 23, 24, 25, 25, 23, 31, 28, 22, 33, 28, 29, 32, 28, 29, 30, 30, 33, 35, 29, 33, 32, 28, 41, 36, 35

Offset

1,3

Comments

{a(n)} is the Pinn F 1,0(n) sequence (see link section).

Links

Table of n, a(n) for n=1..69.

K. Pinn, A Chaotic Cousin Of Conway's Recursive Sequence, arXiv:cond-mat/9808031 [cond-mat.stat-mech], 1998.

Example

a(3)=2 because a(3) = a(3-1-a(3-1))+a(3-a(3-2)) = a(2-1)+a(3-1) = 1+1 = 2.

Mathematica

a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1 - a[n - 1]] + a[n - a[n - 2]]; Table[ a[n], {n, 1, 40}]

Prog

(Python3)
a=[1, 1]
for n in range(100):
    i1=len(a)-1-a[len(a)-1]
    i2=len(a)-a[len(a)-2]
    if i1>=0 and i2>=0 :
        a.append(a[i1]+a[i2])
    else :
        print("Sequence dies. Contains ", n+2, " terms.")
        break
print(a)
(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; va[2] = 1; for (n=3, nn, va[n]=va[n-1-va[n-1]]+va[n-va[n-2]]; ); va; } \\ Michel Marcus, Dec 07 2020

Crossrefs

Cf. A005185, A070867, A046699.

Sequence in context: A349837 A111912 A096288 * A361159 A184995 A136348

Adjacent sequences: A339307 A339308 A339309 * A339311 A339312 A339313

Keyword

nonn

Author

Pablo Hueso Merino, Dec 02 2020

Status

approved