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 A121473 Partial quotients of the continued fraction expansion of the constant A121472 defined by the sums: c = Sum_{n>=1} 1/2^[log_2(e^n)] = Sum_{n>=1} [log(2^n)]/2^n. 3
 0, 1, 6, 146, 8, 37783544111994270385152, 784637716923335095479473680436259502469253233551410733056, 309485009821345068724781056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A "devil's staircase" type of constant has large partial quotients in its continued fraction expansion. See MathWorld link for more information. LINKS Eric Weisstein's World of Mathematics, Devil's Staircase EXAMPLE c=0.857282383103406177511903308509733997590988312093146922257824... The number of 1's in the binary expansion of a(n) is given by the partial quotients of continued fraction of log(2): log(2) = [0; 1, 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, ...] as can be seen by the binary expansions of a(n): a(0) = 0 a(1) = 2^0 a(2) = 2^2 + 2^1 a(3) = 2^7 + 2^4 + 2^1 a(4) = 2^3 a(5) = 2^75 + 2^62 + 2^49 + 2^36 + 2^23 + 2^10 a(6) = 2^189 + 2^101 + 2^13 a(7) = 2^88 a(8) = 2^277 a(9) = 2^1007 + 2^365 a(10) = 2^642 a(11) = 2^1649 a(12) = 2^2291 a(13) = 2^3940 a(14) = 2^26573 + 2^16402 + 2^6231 CROSSREFS Cf. A121472 (constant), A121474 (dual constant), A121475. Sequence in context: A280847 A041271 A196964 * A166837 A166809 A250389 Adjacent sequences:  A121470 A121471 A121472 * A121474 A121475 A121476 KEYWORD cofr,nonn AUTHOR Paul D. Hanna, Aug 01 2006 STATUS approved

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Last modified July 24 21:47 EDT 2021. Contains 346273 sequences. (Running on oeis4.)