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A183164
Least integer k such that k*arctan(n) and k*arctan(n+1) are separated by an integer.
2
1, 5, 4, 3, 5, 7, 9, 11, 13, 19, 27, 41, 85, 2, 61, 43, 33, 29, 25, 23, 21, 19, 36, 17, 32, 15, 43, 28, 41, 13, 76, 50, 37, 24, 35, 46, 57, 101, 11, 97, 64, 53, 42, 31, 51, 71, 111, 20, 69, 49, 78, 29, 67, 105, 38, 47, 103, 56, 74, 83, 101, 128, 182, 299, 9
OFFSET
1,2
COMMENTS
a(n) is the least positive integer for which there is a rational number H with denominator k for which n < tan(H) < n+1.
MATHEMATICA
Table[k=1; While[Floor[k*ArcTan[n+1]]<=k*ArcTan[n], k++]; k, {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 27 2010
STATUS
approved