A272611 a(1)=1; thereafter a(n) = a(n-a(n-1)) + A272612(n-1).

1, 2, 3, 3, 4, 5, 5, 7, 5, 8, 8, 7, 10, 8, 10, 12, 9, 11, 15, 9, 14, 16, 11, 19, 13, 18, 13, 19, 19, 18, 19, 20, 20, 18, 19, 20, 20, 23, 27, 20, 26, 28, 20, 35, 20, 31, 27, 26, 26, 37, 21, 33, 24, 35, 23, 37, 24, 35, 38, 33, 34, 39, 39, 29, 39, 32, 38, 39, 37

Offset: 1

Author

Nathan Fox, May 03 2016

Keywords

• nonn

Comments

Much like the Hofstadter Q-sequence A005185, it is not known if this sequence is defined for all positive n.

Empirically, this sequence appears to grow approximately like n/2 with a lot of noise.

a(n) exists for n<=10^7.

Links

• Nathan Fox, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005185, A272610, A272612, A272613.

Programs

Maple

#Code for A272611, A272612, and A272613
A272611:=proc(n) option remember:
    if n = 1 then
        return 1:
    else
        return A272611(n-A272611(n-1))+A272612(n-1):
    fi:
end:
A272612:=proc(n) option remember:
    if n = 0 then
        return 1:
    elif n = 1 then
        return 1:
    else
        return A272612(n-A272611(n))+A272612(n-A272611(n-1)):
    fi:
end:
A272613:=proc(n) option remember:
    if n = 0 then
        return 1:
    else
        return A272613(n-A272611(n))+A272613(n-A272612(n)):
    fi:
end: