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 A003070 a(n) = ceiling(log_2 n!). (Formerly M2407) 13
 0, 0, 1, 3, 5, 7, 10, 13, 16, 19, 22, 26, 29, 33, 37, 41, 45, 49, 53, 57, 62, 66, 70, 75, 80, 84, 89, 94, 98, 103, 108, 113, 118, 123, 128, 133, 139, 144, 149, 154, 160, 165, 170, 176, 181, 187, 192, 198, 203, 209, 215, 220, 226, 232, 238, 243, 249, 255, 261, 267 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is a lower bound for the minimum number of comparisons needed to sort n elements using a comparison sort (A036604). - Alex Costea, Mar 23 2019 REFERENCES D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 5.3.1. E. Reingold, J. Nievergelt and N. Deo, Combinatorial Algorithms, Prentice-Hall, 1977, section 7.4. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Tianxing Tao, On optimal arrangement of 12 points, pp. 229-234 in Combinatorics, Computing and Complexity, ed. D. Du and G. Hu, Kluwer, 1989. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 MATHEMATICA Array[Ceiling@ Log2[#!] &, 60, 0] (* Michael De Vlieger, Mar 27 2019 *) CROSSREFS Cf. A036604. Essentially the same as A072831. Sequence in context: A092757 A062430 A016040 * A036604 A001768 A089108 Adjacent sequences:  A003067 A003068 A003069 * A003071 A003072 A003073 KEYWORD nonn AUTHOR STATUS approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)