A206584 The least number s having exactly n fours in the continued fraction of sqrt(s).

2, 5, 52, 329, 379, 639, 631, 3937, 1471, 2461, 2524, 6931, 3259, 11809, 5659, 16756, 8779, 14749, 10399, 24721, 14452, 25429, 16669, 31021, 16879, 45301, 21061, 45109, 31054, 72721, 28414, 81061, 40189, 86041, 34654, 109909, 44371, 74881, 42046, 79501, 53551

Offset: 0

Author

T. D. Noe, Mar 19 2012

Keywords

• nonn

Crossrefs

Cf. A206578 (n ones), A206582 (n twos), A206583 (n threes), A206585 (n fives).

Programs

Mathematica

nn = 50; zeros = nn; t = Table[0, {nn}]; k = 2; While[zeros > 0, If[! IntegerQ[Sqrt[k]], cnt = Count[ContinuedFraction[Sqrt[k]][[2]], 4]; If[cnt <= nn && t[[cnt]] == 0, t[[cnt]] = k; zeros--]]; k++]; Join[{2}, t]
With[{tbl=Table[{n,Count[If[IntegerQ[Sqrt[n]],{1},ContinuedFraction[Sqrt[n]][[2]]],4]},{n,2,110000}]},Table[SelectFirst[tbl,#[[2]]==k&],{k,0,40}]][[All,1]] (* Harvey P. Dale, Oct 05 2022 *)