A309650 a(1) = 3, a(2) = 1, a(3) = 4, a(4) = 2; a(n) = a(n-a(n-2)) + a(n-a(n-3)) for n > 4.

3, 1, 4, 2, 5, 3, 6, 9, 7, 5, 3, 11, 14, 7, 5, 8, 16, 19, 7, 5, 8, 21, 24, 12, 5, 8, 26, 29, 12, 5, 8, 31, 34, 12, 5, 13, 36, 39, 12, 5, 13, 41, 44, 12, 5, 13, 46, 49, 17, 5, 13, 51, 54, 17, 5, 13, 56, 59, 17, 5, 13, 61, 64, 17, 5, 18, 66, 69, 17, 5, 18, 71, 74, 17, 5, 18, 76, 79, 17, 5, 18, 81, 84, 22, 5

Offset: 1

Author

Altug Alkan and Nathan Fox, Aug 11 2019

Keywords

• nonn
• easy

Comments

A well-defined quasi-periodic solution for recurrence (a(n) = a(n-a(n-2)) + a(n-a(n-3))).

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Altug Alkan, Nathan Fox, Orhan Ozgur Aybar, Zehra Akdeniz, On Some Solutions to Hofstadter's V-Recurrence, arXiv:2002.03396 [math.DS], 2020.

Crossrefs

Cf. A063892, A244477, A309492, A309567.

Programs

Magma

I:=[3,1,4,2]; [n le 4 select I[n] else  Self(n-Self(n-2)) + Self(n-Self(n-3)): n in [1..90]]; // Marius A. Burtea, Aug 11 2019

Mathematica

Nest[Append[#, #[[-#[[-2]] ]] + #[[-#[[-3]] ]]] &, {3, 1, 4, 2}, 81] (* Michael De Vlieger, May 08 2020 *)

PARI

q=vector(100); q[1]=3; q[2]=1; q[3]=4; q[4]=2; for(n=5, #q, q[n] = q[n-q[n-2]] + q[n-q[n-3]]); q

Formula

For k >= 1:

a(5*k) = 5,

a(5*k+1) = 5*floor(sqrt(k)+1/2)-2,

a(5*k+2) = 5*k+1,

a(5*k+3) = 5*k+4,

a(5*k+4) = 5*floor(sqrt(k))+2.