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 A121475 Partial quotients of the continued fraction expansion of the constant A121474 defined by the sums: c = Sum_{n>=1} [log_2(e^n)]/2^n = Sum_{n>=1} 1/2^[log(2^n)]. 3
 2, 3, 42, 4, 4512412933881984, 2722258935367507708887588480171556995584, 2305843009213693952, 6277101735386680763835789423207666416102355444464034512896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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=2.330724070450097847357272640178093538603148610143875650321... The number of 1's in the binary expansion of a(n) is given by the partial quotients of continued fraction of 1/log(2): 1/log(2) = [1; 2, 3, 1, 6, 3, 1, 1, 2, 1, 1, 1, 1, 3, 10, 1, ...] as can be seen by the binary expansion of a(n): a(0) = 2^1 a(1) = 2^1 + 2^0 a(2) = 2^5 + 2^3 + 2^1 a(3) = 2^2 a(4) = 2^52 + 2^43 + 2^34 + 2^25 + 2^16 + 2^7 a(5) = 2^131 + 2^70 + 2^9 a(6) = 2^61 a(7) = 2^192 a(8) = 2^698 + 2^253 a(9) = 2^445 a(10) = 2^1143 a(11) = 2^1588 a(12) = 2^2731 a(13) = 2^18419 + 2^11369 + 2^4319 CROSSREFS Cf. A121474 (decimal expansion), A121472 (dual constant), A121473. Sequence in context: A123993 A271331 A101821 * A334533 A196874 A087571 Adjacent sequences:  A121472 A121473 A121474 * A121476 A121477 A121478 KEYWORD cofr,nonn AUTHOR Paul D. Hanna, Aug 01 2006 STATUS approved

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Last modified July 27 13:36 EDT 2021. Contains 346306 sequences. (Running on oeis4.)