A206582 The least nonsquare number s having exactly n twos in the periodic part of the continued fraction of sqrt(s).

5, 2, 19, 45, 71, 153, 199, 589, 301, 989, 526, 1711, 739, 1633, 631, 3886, 1324, 4897, 2524, 7021, 2374, 4189, 2311, 10033, 3571, 3901, 2326, 8869, 4789, 10873, 6301, 10921, 6451, 11929, 6841, 12709, 7996, 13561, 7351, 19177, 9949, 16969, 12286, 22969, 11341

Offset

0,1

Links

Table of n, a(n) for n=0..44.

Maple

V:= Array(0..50):  count:= 0:
with(NumberTheory):
for i from 2 while count < 51 do
  if issqr(i) then next fi;
  cf:= Term(ContinuedFraction(sqrt(i)), periodic);
  v:= numboccur(cf[2], 2);
  if v <= 50 and V[v] = 0 then
    V[v]:= i; count:= count+1;
  fi;
od:
convert(V, list); # Robert Israel, May 13 2024

Mathematica

nn = 50; zeros = nn; t = Table[0, {nn}]; k = 2; While[zeros > 0, If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][[2]], 2]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = k; zeros--]]; k++]; Join[{5}, t]

Crossrefs

Cf. A206578 (n ones), A206583 (n threes), A206584 (n fours), A206585 (n fives).

Sequence in context: A356330 A306198 A327316 * A276533 A303685 A189746

Adjacent sequences: A206579 A206580 A206581 * A206583 A206584 A206585

Keyword

nonn

Author

T. D. Noe, Mar 19 2012

Extensions

Corrected by Robert Israel, May 13 2024

Status

approved