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 A190868 Let C(n) be the expected length of the longest carry chain when two n-bit binary numbers are added; sequence gives a(n) = 2^(2n-1)*C(n). 1
 0, 14, 106, 598, 3002, 14142, 64106, 283166, 1228346, 5257966, 22281738, 93689246, 391512666, 1627925006, 6741353258, 27821715326, 114493140090, 470023545198, 1925545015370, 7874137194718, 32148981709466, 131077794504654, 533774656417642, 2171261671337534, 8823512782678714, 35825200435380270 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS The addition is carried out by a parallel adder as described by J. von Neumann. LINKS Volker Claus, Die mittlere Additionsdauer eines Paralleladdierwerks, Acta Informat. 2 (1973), 283-291. D. E. Knuth, The average time for carry propagation, Nederl. Akad. Wetensch. Indag. Math., 81 (2) (1978), 238-242. Nicholas Pippenger, Analysis of carry propagation in addition: an elementary approach, J. Algorithms 42 (2002), 317-333. FORMULA C(n) = E(n)-1, where E(n) is defined in A190866. EXAMPLE C(n) for n >= 2: 0, 7/16, 53/64, 299/256, 1501/1024, 7071/4096, 32053/16384, 141583/65536, ... MAPLE See A190866. CROSSREFS Cf. A190866. Sequence in context: A285752 A076128 A206761 * A125351 A126509 A200056 Adjacent sequences:  A190865 A190866 A190867 * A190869 A190870 A190871 KEYWORD nonn,frac AUTHOR R. J. Mathar and N. J. A. Sloane, May 22 2011 STATUS approved

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Last modified June 30 18:10 EDT 2022. Contains 354945 sequences. (Running on oeis4.)