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

1, 4, 8, 16, 32, 64, 96, 128, 320, 512, 2048, 2304, 19922944, 41943040, 167772160

Offset

1,2

Comments

The corresponding values of k are given in A352917.

This is a subset of A352203.

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.

Links

Table of n, a(n) for n=1..15.

Example

Let c(k) denote A109812(k). The first 15 record high-points of c(k)/k are as follows:
[c(k)/k, k, c(k), "binary(c(n))"]
[1.000000000, 1, 1, "1"]
[1.333333333, 3, 4, "100"]
[1.600000000, 5, 8, "1000"]
[2.000000000, 8, 16, "10000"]
[2.133333333, 15, 32, "100000"]
[2.206896552, 29, 64, "1000000"]
[2.400000000, 40, 96, "1100000"]
[2.560000000, 50, 128, "10000000"]
[2.962962963, 108, 320, "101000000"]
[3.121951220, 164, 512, "1000000000"]
[3.155624037, 649, 2048, "100000000000"]
[3.539170507, 651, 2304, "100100000000"]
[3.616182275, 5509386, 19922944, "1001100000000000000000000"]
[3.721304271, 11271059, 41943040, "10100000000000000000000000"]
[3.727433952, 45010096, 167772160, "1010000000000000000000000000"]
The values of k and c(k) form A352917 and the present sequence.

Crossrefs

Cf. A109812, A352203, A352204, A352917.

Sequence in context: A121986 A285906 A172042 * A145108 A108569 A342868

Adjacent sequences: A352915 A352916 A352917 * A352919 A352920 A352921

Keyword

nonn,more

Author

David Broadhurst, Aug 17 2022 (entry created by N. J. A. Sloane, Apr 21 2022)

Status

approved