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URL: https://oeis.org/A355169

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A355169
Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168.
2
2, 14, 18, 22, 31, 41, 46, 82, 117, 132, 172, 189, 243, 252, 262, 281, 291, 301, 311, 332, 353, 374, 385, 396, 407, 441, 464, 560, 585, 610, 623, 636, 649, 662, 675, 688, 715, 742, 769, 783, 797, 825, 839, 853, 896, 925, 940, 1060, 1075, 1106, 1137, 1153
OFFSET
1,1
COMMENTS
See A355160.
FORMULA
a(n) = floor(m^(3/2)), where m = A355160(n).
EXAMPLE
a(1) = 2 corresponds to 2/2 < sqrt(2) < 3/2.
a(2) = 14 corresponds to 14/6 < sqrt(6) < 15/6.
a(3) = 18 corresponds to 18/7 < sqrt(7) < 19/7.
MATHEMATICA
u = Select[Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &] (* A355159 *)
v = Select[Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &] (* A355160 *)
Floor[u^(3/2)] (* A355168: numerators for fractions h/k <= sqrt(k) *)
Floor[v^(3/2)] (* A355169: numerators for fractions h/k > sqrt(k) *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 26 2022
STATUS
approved