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A344906 Decimal expansion of Sum_{k>=0} arctan(1/2^k). 1
1, 7, 4, 3, 2, 8, 6, 6, 2, 0, 4, 7, 2, 3, 4, 0, 0, 0, 3, 5, 0, 4, 3, 3, 7, 6, 5, 6, 1, 3, 6, 4, 1, 6, 2, 8, 5, 8, 1, 3, 8, 3, 1, 1, 8, 5, 4, 2, 8, 2, 0, 6, 5, 2, 3, 0, 0, 4, 5, 6, 9, 5, 7, 2, 0, 5, 6, 5, 5, 1, 7, 6, 5, 2, 2, 7, 4, 9, 2, 0, 5, 5, 8, 1, 6, 5, 8, 6, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This number can be interpreted geometrically as the angle in radians of a fan made of stacked right triangles, with the length to height ratio doubling each successive triangle as seen in the illustration.

LINKS

Table of n, a(n) for n=1..89.

Daniel Hoyt, Illustration of this angle's arctan relationship.

FORMULA

Equals Sum_{k>=1} (-1)^(k+1)*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)).

EXAMPLE

1.743286620472340003...

MAPLE

Digits:= 140:

evalf(sum(arccot(2^k), k=0..infinity));  # Alois P. Heinz, Jun 02 2021

PROG

(PARI) suminf(k=0, atan(1/2^k))

(PARI) sumalt(k=1, ((-1)^(k+1))*2^(2*k-1)/((2^(2*k-1)-1)*(2*k-1)))

CROSSREFS

Cf. A003881, A073000, A195727, A195782.

Sequence in context: A019857 A296474 A194705 * A243309 A244817 A303612

Adjacent sequences:  A344903 A344904 A344905 * A344907 A344908 A344909

KEYWORD

nonn,cons

AUTHOR

Daniel Hoyt, Jun 01 2021

STATUS

approved

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Last modified January 26 12:17 EST 2022. Contains 350598 sequences. (Running on oeis4.)