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 A299613 Decimal expansion of 2*W(1), where W is the Lambert W function (or PowerLog); see Comments. 21
 1, 1, 3, 4, 2, 8, 6, 5, 8, 0, 8, 1, 9, 5, 6, 7, 7, 4, 5, 9, 9, 9, 9, 3, 7, 3, 2, 4, 4, 2, 0, 7, 1, 1, 0, 9, 9, 5, 0, 7, 6, 3, 1, 5, 7, 4, 3, 7, 3, 0, 2, 5, 0, 1, 6, 2, 7, 0, 2, 6, 2, 1, 5, 8, 4, 4, 6, 0, 9, 1, 5, 8, 6, 1, 7, 3, 3, 6, 9, 1, 3, 3, 3, 8, 6, 4 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Lambert W function satisfies the functional equations W(x) + W(y) = W(x*y(1/W(x) + 1/W(y)) = log(x*y)/(W(x)*W(y)) for x and y greater than -1/e, so that 2*W(1) = W(2/W(1)) = -2*log(W(1)). Guide to related constants: -------------------------------------------- x        y      W(x) + W(y)  e^(W(x) + W(y)) -------------------------------------------- 1        1        A299613        A299614 1        2        A299615        A299616 1        e        A030178        A299617 e        e        2 exactly      e^2 exactly 1        1/e      A299618        A299619 1        3        A299620        A299621 1        1/2      A299622        A299623 1/2      1/2      A126583        A099954 2        2        A299624        A299625 3        3        A299626        A299627 1/3      1/3      A299628        A299629 3/2      3/2      A299630        A299631 e/2      e/2      A299632        A299633 LINKS Clark Kimberling, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Lambert W-Function FORMULA Equals 2*A030178. EXAMPLE 2*W(1) = 1.13428658081956774599993... MATHEMATICA w[x_] := ProductLog[x]; x = 1; y = 1; u = N[w[x] + w[y], 100] RealDigits[u, 10][[1]]  (* A299613 *) RealDigits[2 ProductLog[1], 10, 111][[1]] (* Robert G. Wilson v, Mar 02 2018 *) PROG (PARI) 2*lambertw(1) \\ G. C. Greubel, Mar 07 2018 CROSSREFS Cf. A299614-A299633. Sequence in context: A020502 A252896 A266562 * A066892 A143053 A220508 Adjacent sequences:  A299610 A299611 A299612 * A299614 A299615 A299616 KEYWORD nonn,cons,easy AUTHOR Clark Kimberling, Mar 01 2018 STATUS approved

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Last modified January 24 18:36 EST 2021. Contains 340411 sequences. (Running on oeis4.)