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A337371
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Integers k with abs(sin(k)) < 1/k.
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3
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1, 3, 22, 44, 355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195, 312689, 1146408, 5419351, 10838702, 6167950454, 21053343141, 42106686282, 63160029423, 84213372564, 105266715705, 8958937768937, 17917875537874, 428224593349304, 856449186698608, 6134899525417045
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OFFSET
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1,2
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COMMENTS
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The values > 1 appear to be a subset of the numerators of continued fractions of Pi (A002485) (and/or Pi/2: A096456) and their multiples. Is it possible to find a term k here but not in |A332095| (k |tan k| < 1)? - M. F. Hasler, Oct 09 2020
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LINKS
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MATHEMATICA
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Select[Range[3200], Abs[Sin[#]] < 1/# &] (* Amiram Eldar, Aug 25 2020 *)
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PROG
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(Python)
import numpy as np
for x in range(1, 10**9):
if np.abs(np.sin(x)) < 1/x:
print(x, end=", ")
(PARI) print1(1); apply( n-> forstep(n=n, oo, n, abs(sin(n))<1/n||return; print1(", "n)), contfracpnqn(c=contfrac(Pi), #c)[1, ]); \\ M. F. Hasler, Oct 09 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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