A113605 a(1) = a(2) = a(3) = 1; a(n) = a(n-3) + gcd(a(n-1), a(n-2)).

1, 1, 1, 2, 2, 3, 3, 5, 4, 4, 9, 5, 5, 14, 6, 7, 15, 7, 8, 16, 15, 9, 19, 16, 10, 21, 17, 11, 22, 28, 13, 23, 29, 14, 24, 31, 15, 25, 36, 16, 29, 37, 17, 30, 38, 19, 49, 39, 20, 50, 49, 21, 57, 52, 22, 59, 53, 23, 60, 54, 29, 61, 55, 30, 66, 61, 31, 67, 62, 32, 69, 63, 35, 76, 64

Offset: 1

Author

Leroy Quet, Jan 26 2006

Keywords

• nonn

Examples

			a(16) = a(13) + gcd(a(15), a(14)) = 5 + gcd(6,14) = 7.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

a[1]:=1: a[2]:=1: a[3]:=1: for n from 4 to 100 do a[n]:=a[n-3]+gcd(a[n-1],a[n-2]) od: seq(a[n],n=1..90); # Emeric Deutsch, Feb 01 2006

Mathematica

a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 3] + GCD[a[n - 1], a[n - 2]]; Array[a, 75] (* Robert G. Wilson v *)
nxt[{a_,b_,c_}]:={b,c,a+GCD[b,c]}; Transpose[NestList[nxt,{1,1,1},80]] [[1]] (* Harvey P. Dale, Sep 02 2015 *)

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Feb 01 2006