A316627 a(1)=2, a(2)=3; a(n) = a(n+1-a(n-1))+a(n-a(n-2)) for n > 2.

2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 40, 40, 40, 41, 42, 42

Offset: 1

Author

Nathan Fox, Jul 08 2018

Keywords

• nonn

Comments

This sequence increases slowly.

If k is not a power of 2, k occurs A001511(k) times. Otherwise, k occurs A001511(k)-1 times.

This is the meta-Fibonacci sequence for s=-1.

References

• B. W. Conolly, "Meta-Fibonacci sequences," in S. Vajda, editor, Fibonacci and Lucas Numbers and the Golden Section. Halstead Press, NY, 1989, pp. 127-138. See Eq. (2).

Links

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

Crossrefs

Cf. A001511, A005185, A006949, A046699.

Programs

GAP

a:=[2,3];; for n in [3..75] do a[n]:=a[n+1-a[n-1]]+a[n-a[n-2]]; od; a; # Muniru A Asiru, Jul 09 2018

Magma

I:=[2,3]; [n le 2 select I[n] else Self(n+1-Self(n-1))+Self(n-Self(n-2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018

Maple

A316627:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 2: elif n = 2 then 3: else A316627(n + 1-A316627(n-1)) + A316627(n-A316627(n-2)): fi: end:

Formula

a(n+1)-a(n)=1 or 0.

a(n)/n -> C=1/2.