A352918 -id:A352918 - cp's OEIS frontend

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

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

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.

			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.

Cf. A109812, A352203, A352204, A352918.

cp's OEIS Frontend

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

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