A352917 - OEIS

%I #12 Apr 22 2022 17:06:11

%S 1,3,5,8,15,29,40,50,108,164,649,651,5509386,11271059,45010096

%N Indices k where A109812(k)/k reaches a new high point.

%C The corresponding values of A109812(k) are given in A352918.

%C This is a subset of A352204.

%C 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 Let c(k) denote A109812(k). The first 15 record high-points of c(k)/k are as follows:

%e [c(k)/k, k, c(k), "binary(c(n))"]

%e [1.000000000, 1, 1, "1"]

%e [1.333333333, 3, 4, "100"]

%e [1.600000000, 5, 8, "1000"]

%e [2.000000000, 8, 16, "10000"]

%e [2.133333333, 15, 32, "100000"]

%e [2.206896552, 29, 64, "1000000"]

%e [2.400000000, 40, 96, "1100000"]

%e [2.560000000, 50, 128, "10000000"]

%e [2.962962963, 108, 320, "101000000"]

%e [3.121951220, 164, 512, "1000000000"]

%e [3.155624037, 649, 2048, "100000000000"]

%e [3.539170507, 651, 2304, "100100000000"]

%e [3.616182275, 5509386, 19922944, "1001100000000000000000000"]

%e [3.721304271, 11271059, 41943040, "10100000000000000000000000"]

%e [3.727433952, 45010096, 167772160, "1010000000000000000000000000"]

%e The values of k and c(k) form the present sequence and A352918.

%Y Cf. A109812, A352203, A352204, A352918.

%K nonn,more

%O 1,2

%A _David Broadhurst_, Aug 17 2022 (entry created by _N. J. A. Sloane_, Apr 21 2022)