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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000040, A133058.

Sequence in context: A226895 A306996 A166007 * A087497 A085767 A082127

Adjacent sequences: A372745 A372746 A372747 * A372749 A372750 A372751

Keyword

nonn,changed

Author

Ctibor O. Zizka, May 12 2024

Status

approved