

A187261


Least number k such that the continued fraction expansion of its square root contains the first n natural numbers.


2



1, 2, 14, 19, 211, 463, 634, 1057, 1951, 2326, 4156, 5149, 8254, 9811, 10651, 21319, 15814, 19609, 29527, 42379, 46006, 58171, 89959, 97579, 144271, 135319, 164431, 217519, 201919, 230101, 216451, 285814, 307759, 323359
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OFFSET

1,2


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..100


EXAMPLE

a(1) is 1.
a(2) is 2 because the cf of sqrt(2) = 1, 2, 2, .., .
a(3) is 14 because the cf of sqrt(14) = 3, {1, 2, 1, 6},
a(4) is 19 because the cf of sqrt(19) = 4, {2, 1, 3, 1, 2, 8},
a(5) is 211 because the cf of sqrt(211) = 14, {1, 1, 9, 5, 1, 2, 2, 1, 1, 4, 3, 1, 13, 1, 3, 4, 1, 1, 2, 2, 1, 5, 9, 1, 1, 28} which includes the natural numbers 1 through 5 and there does not exist any integer less than 211 which has this characteristics, etc.


MATHEMATICA

f[n_] := Block[{cf = Union@ Flatten@ ContinuedFraction@ Sqrt@ n, k = 1}, While[k <= Length[cf] && k == cf[[k]], k++]; k  1]; t = Table[ 0, {100}]; k = 1; While[k < 10^7, a = f@ k; If[a <= Length[t] && t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; t


CROSSREFS

Cf. A000027, A187142.
Sequence in context: A059205 A298002 A217075 * A101398 A131221 A138047
Adjacent sequences: A187258 A187259 A187260 * A187262 A187263 A187264


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, Mar 07 2011


STATUS

approved



