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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)).

%I A372748 #22 Feb 12 2025 03:32:28
%S A372748 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,
%T A372748 25,25,25,25,25,25,25,30,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,
%U A372748 31,31,31,31,31,31,31,31,31,31,31,61,61,61,61,61,61,61,61
%N 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)).
%C A372748 a(n) = n/2 for n from {4,6,10,26,62,122,298,626,1094,2186,...}.
%H A372748 Paolo Xausa, <a href="/A372748/b372748.txt">Table of n, a(n) for n = 1..10000</a>
%e A372748 a(1) = 3.
%e A372748 a(2) = 3 because GCD(1,3) = 1.
%e A372748 a(3) = 3 because GCD(2,3) = 1.
%e A372748 a(4) = 3 - 3/GCD(3,3) = 2.
%e A372748 and so on.
%t A372748 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 *)
%t A372748 FoldList[If[CoprimeQ[#, #2], #, #2 - #/GCD[#, #2]] &, 3, Range[100]] (* _Paolo Xausa_, Feb 12 2025 *)
%Y A372748 Cf. A000040, A133058.
%K A372748 nonn
%O A372748 1,1
%A A372748 _Ctibor O. Zizka_, May 12 2024