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

0,1

Links

Table of n, a(n) for n=0..40.

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 *)

Crossrefs

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

Sequence in context: A208206 A005114 A216079 * A268286 A081090 A330282

Adjacent sequences: A206581 A206582 A206583 * A206585 A206586 A206587

Keyword

nonn

Author

T. D. Noe, Mar 19 2012

Status

approved