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A146477 Numbers k for which A146326(k) is different from A146326(j) for j < k.

%I A146477 #10 May 04 2021 09:02:25
%S A146477 2,5,6,17,18,31,41,43,73,89,94,106,118,151,172,193,211,241,265,268,
%T A146477 331,334,337,379,394,409,421,433,463,489,521,526,601,604,619,634,673,
%U A146477 694,718,721,751,769,886,919,929,937,1033,1039,1114,1174,1201,1249,1291,1321,1324,1471,1516,1579,1609
%N A146477 Numbers k for which A146326(k) is different from A146326(j) for j < k.
%C A146477 This sequence is sorted A146343.
%C A146477 Original name was: a(n) = smallest numbers which continued fractions have different period.
%H A146477 Robert Israel, <a href="/A146477/b146477.txt">Table of n, a(n) for n = 1..700</a>
%p A146477 f:= proc(n) if issqr(n) then 0 else nops(numtheory:-cfrac((1+sqrt(n))/2,periodic,quotients)[2]) fi end proc:
%p A146477 S:= {0}: R:= NULL: count:= 0:
%p A146477 for n from 2 while count < 30 do
%p A146477   v:= f(n);
%p A146477   if not member(v,S) then
%p A146477      count:= count+1; R:= R, n; S:= S union {v};
%p A146477   fi
%p A146477 od:
%p A146477 R; # _Robert Israel_, May 02 2021
%t A146477 $MaxExtraPrecision = 300; s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[n])/2, 1000]; If[Length[k] < 190, AppendTo[aa, 0], m = 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; AppendTo[aa, m]], {n, 1, 1200}]; Print[aa]; bb = {}; Do[k = 1; yes = 0; Do[If[aa[[k]] == n && yes == 0, AppendTo[bb, k]; yes = 1], {k, 1, Length[aa]}], {n, 1, 22}]; Sort[bb]
%Y A146477 Cf. A000290, A078370, A146326-A146345, A146348-A146360, A146363.
%K A146477 nonn
%O A146477 1,1
%A A146477 _Artur Jasinski_, Oct 30 2008
%E A146477 19 replaced by 18, 331 and 334 inserted by _R. J. Mathar_, Nov 08 2008
%E A146477 Name clarified by _Robert Israel_, May 02 2021