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

2, 5, 6, 17, 18, 31, 41, 43, 73, 89, 94, 106, 118, 151, 172, 193, 211, 241, 265, 268, 331, 334, 337, 379, 394, 409, 421, 433, 463, 489, 521, 526, 601, 604, 619, 634, 673, 694, 718, 721, 751, 769, 886, 919, 929, 937, 1033, 1039, 1114, 1174, 1201, 1249, 1291, 1321, 1324, 1471, 1516, 1579, 1609

Offset

1,1

Comments

This sequence is sorted A146343.

Original name was: a(n) = smallest numbers which continued fractions have different period.

Links

Robert Israel, Table of n, a(n) for n = 1..700

Maple

f:= proc(n) if issqr(n) then 0 else nops(numtheory:-cfrac((1+sqrt(n))/2, periodic, quotients)[2]) fi end proc:
S:= {0}: R:= NULL: count:= 0:
for n from 2 while count < 30 do
  v:= f(n);
  if not member(v, S) then
     count:= count+1; R:= R, n; S:= S union {v};
  fi
od:
R; # Robert Israel, May 02 2021

Mathematica

$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]

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360, A146363.

Sequence in context: A342488 A098871 A227623 * A348439 A166753 A319756

Adjacent sequences: A146474 A146475 A146476 * A146478 A146479 A146480

Keyword

nonn

Author

Artur Jasinski, Oct 30 2008

Extensions

19 replaced by 18, 331 and 334 inserted by R. J. Mathar, Nov 08 2008

Name clarified by Robert Israel, May 02 2021

Status

approved