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A352918 Values of A109812(k) where A109812(k)/k reaches a new high point.

%I A352918 #11 Apr 22 2022 17:07:09
%S A352918 1,4,8,16,32,64,96,128,320,512,2048,2304,19922944,41943040,167772160
%N A352918 Values of A109812(k) where A109812(k)/k reaches a new high point.
%C A352918 The corresponding values of k are given in A352917.
%C A352918 This is a subset of A352203.
%C A352918 The slow growth of A109812(k)/k (see Examples section) suggests that A109812(k)/k is bounded. That is, it appears there is a constant c (between 3.7 and 4) such that A109812(k) < c*k for all k.
%e A352918 Let c(k) denote A109812(k). The first 15 record high-points of c(k)/k are as follows:
%e A352918 [c(k)/k, k, c(k), "binary(c(n))"]
%e A352918 [1.000000000, 1, 1, "1"]
%e A352918 [1.333333333, 3, 4, "100"]
%e A352918 [1.600000000, 5, 8, "1000"]
%e A352918 [2.000000000, 8, 16, "10000"]
%e A352918 [2.133333333, 15, 32, "100000"]
%e A352918 [2.206896552, 29, 64, "1000000"]
%e A352918 [2.400000000, 40, 96, "1100000"]
%e A352918 [2.560000000, 50, 128, "10000000"]
%e A352918 [2.962962963, 108, 320, "101000000"]
%e A352918 [3.121951220, 164, 512, "1000000000"]
%e A352918 [3.155624037, 649, 2048, "100000000000"]
%e A352918 [3.539170507, 651, 2304, "100100000000"]
%e A352918 [3.616182275, 5509386, 19922944, "1001100000000000000000000"]
%e A352918 [3.721304271, 11271059, 41943040, "10100000000000000000000000"]
%e A352918 [3.727433952, 45010096, 167772160, "1010000000000000000000000000"]
%e A352918 The values of k and c(k) form A352917 and the present sequence.
%Y A352918 Cf. A109812, A352203, A352204, A352917.
%K A352918 nonn,more
%O A352918 1,2
%A A352918 _David Broadhurst_, Aug 17 2022 (entry created by _N. J. A. Sloane_, Apr 21 2022)