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A249022 Decimal expansion of Sine Euler constant. 1
4, 6, 6, 5, 9, 9, 3, 0, 6, 2, 0, 3, 7, 2, 9, 2, 6, 5, 2, 2, 1, 7, 3, 4, 2, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The Sine Euler constant is introduced here as the limit as n increases without bound of sum{sin(1/k), k = 1..n} - integral{sin(1/x) over [1,n]}; this is analogous to the Euler constant, defined as the limit of sum{1/k, k = 1..n} - integral{1/x over [1,n]}.

LINKS

Table of n, a(n) for n=0..26.

EXAMPLE

Sine Euler constant = 0.466599306203729265221734220...

MATHEMATICA

f = DifferenceRoot[Function[{\[FormalY], \[FormalN]}, {((2 \[FormalN] - z) (2 \[FormalN] - (z + 1))) \[FormalY][\[FormalN]] + \[FormalY][1 + \[FormalN]] == 0, \[FormalY][1] == -1}]];

(Total[Table[1/((-1)^(n + 1) (2 n - 1)!) HarmonicNumber[k, 2 n - 1], {n, 50}]] /. k -> #) - (CosIntegral[1] - CosIntegral[1/#] - Sin[1] + # Sin[1/#]) &[N[10^35, 40]]

RealDigits[t][[1]]

(* Peter J. C. Moses, Oct 20 2014 *)

CROSSREFS

Cf. A001620 (Euler constant), A249023 (Tangent Euler constant).

Sequence in context: A155907 A081261 A251738 * A270541 A046262 A147862

Adjacent sequences:  A249019 A249020 A249021 * A249023 A249024 A249025

KEYWORD

nonn,easy,cons

AUTHOR

Clark Kimberling, Oct 22 2014

STATUS

approved

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Last modified February 24 00:19 EST 2020. Contains 332195 sequences. (Running on oeis4.)