A372748 a(1) = 3; for n > 1, a(n) = a(n - 1) if GCD(n - 1, a(n - 1)) = 1, otherwise a(n) = n - 1 - a(n - 1) / GCD(n - 1, a(n - 1)).

3, 3, 3, 2, 3, 3, 5, 5, 5, 5, 9, 9, 9, 9, 9, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 25, 25, 25, 25, 25, 25, 25, 25, 25, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 61, 61, 61, 61, 61, 61, 61, 61

Offset: 1

Author

Ctibor O. Zizka, May 12 2024

Keywords

• nonn

Comments

a(n) = n/2 for n from {4,6,10,26,62,122,298,626,1094,2186,...}.

Examples

			a(1) = 3.
a(2) = 3 because GCD(1,3) = 1.
a(3) = 3 because GCD(2,3) = 1.
a(4) = 3 - 3/GCD(3,3) = 2.
and so on.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A133058.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[GCD[n,a]==1,a,n-a/GCD[n,a]]}; NestList[nxt,{1,3},70][[;;,2]] (* Harvey P. Dale, Feb 11 2025 *)
FoldList[If[CoprimeQ[#, #2], #, #2 - #/GCD[#, #2]] &, 3, Range[100]] (* Paolo Xausa, Feb 12 2025 *)