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 A229484 Pairs of numbers (m,k) such that 2^m/(m+1) < binomial(m,k) <= 2^m/m and k < m/2. 3
 2, 1, 4, 1, 19, 6, 61, 23, 89, 35, 130, 53, 139, 57, 291, 126, 343, 150, 521, 233, 712, 323, 788, 359, 929, 426, 950, 436, 971, 446, 1080, 498, 1289, 598, 1387, 645, 1593, 744, 1728, 809, 1925, 904, 1954, 918, 2254, 1063, 2508, 1186, 2842, 1348, 3087, 1467 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sun conjectures that there are an infinite number of pairs (m,k) that satisfy this inequality. LINKS T. D. Noe, Table of n, a(n) for n = 1..208 (for m < 10^5) Zhi-Hong Sun, Inequalities for binomial coefficients, arXiv:1310.0353, Oct 02 2013 MATHEMATICA t = {}; Do[k = Floor[m/2]; While[b = Binomial[m, k]; k > 0 && b*m > 2^m, k--]; If[b*(m+1) > 2^m, AppendTo[t, {m, k}]], {m, 1000}]; Flatten[t] CROSSREFS Cf. A007318 (binomial coefficients), A229485 (m), A229486 (k). Sequence in context: A024539 A128271 A092891 * A080212 A186727 A145998 Adjacent sequences:  A229481 A229482 A229483 * A229485 A229486 A229487 KEYWORD nonn AUTHOR T. D. Noe, Oct 04 2013 STATUS approved

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Last modified February 25 05:01 EST 2020. Contains 332217 sequences. (Running on oeis4.)