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A355168
Numerators of best lower approximates h/k to sqrt(k); complement of A355169.
2
1, 5, 8, 11, 27, 36, 52, 58, 64, 70, 76, 89, 96, 103, 110, 125, 140, 148, 156, 164, 181, 198, 207, 216, 225, 234, 272, 322, 343, 364, 419, 430, 453, 476, 488, 500, 512, 524, 536, 548, 573, 598, 702, 729, 756, 811, 868, 882, 911, 955, 970, 985, 1000, 1015
OFFSET
1,2
COMMENTS
See A355159.
FORMULA
a(n) = floor(m^(3/2)), where m = A355159(n).
EXAMPLE
The first five best lower approximates (to sqrt(1), sqrt(3), sqrt(4), sqrt(5), sqrt(9), respectively) are 1/1, 5/3, 8/4, 11/5, 27/9; these are A355168(n)/A355159(n), for n=1..5..
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