A352917 Indices k where A109812(k)/k reaches a new high point.

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

Offset

1,2

Comments

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

This is a subset of A352204.

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 the present sequence and A352918.

Crossrefs

Cf. A109812, A352203, A352204, A352918.

Sequence in context: A215327 A208723 A285010 * A099846 A141775 A056765

Adjacent sequences: A352914 A352915 A352916 * A352918 A352919 A352920

Keyword

nonn,more

Author

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

Status

approved