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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 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.)