A352920 -id:A352920 - cp's OEIS frontend

A352923 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives r(n).

1, 2, 4, 4, 6, 7, 8, 9, 10, 11, 12, 14, 14, 16, 18, 18, 18, 20

Offset: 1

David Broadhurst, Aug 17 2022 (entry created by N. J. A. Sloane, Apr 24 2022)

The sequences m, p, r are well-defined since every number appears in A109812, and if A109812(s) = 2^n - 1, then by definition both A109812(s-1) and A109812(s+1) must be multiples of 2^n.
The sequences m, p, r are discussed in A352920.
Conjecture: r(n) >= n for n >= 1.

Cf. A109812, A113233, A352203, A352204, A352336, A352359, A352917-A352922.

A352922 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives m(n).

Original entry on oeis.org

0, 1, 4, 3, 6, 6, 8, 8, 10, 10, 11, 14, 14, 16, 18, 18, 18, 20

Offset: 1

David Broadhurst, Aug 17 2022 (entry created by N. J. A. Sloane, Apr 24 2022)

The sequences m, p, r are well-defined since every number appears in A109812, and if A109812(s) = 2^n - 1, then by definition both A109812(s-1) and A109812(s+1) must be multiples of 2^n.
The sequences m, p, r are discussed in A352920.
(We assume A109812(0)=0 in order to get m(1)=0.)

Cf. A109812, A113233, A352203, A352204, A352336, A352359, A352917-A352923.

A352919 Indices k where k/A109812(k) reaches a new high point.

Original entry on oeis.org

1, 4, 9, 16, 76, 162, 418, 1892, 19094, 19298, 20059, 84653, 174566, 1688099

Offset: 1

David Broadhurst, Aug 17 2022 (entry created by N. J. A. Sloane, Apr 23 2022)

The corresponding values of A109812(k) are given in A352920.

This is a subset of A352359.

			Let c(k) denote A109812(k). The first 14 record high-points of k/c(k) are as follows:
[k/c(k), k, c(k), "binary(c(n))"]
[1.000000000 1 1 "1"]
[1.333333333 4 3 "11"]
[1.500000000 9 6 "110"]
[2.285714286 16 7 "111"]
[2.451612903 76 31 "11111"]
[2.571428571 162 63 "111111"]
[3.291338583 418 127 "1111111"]
[3.702544031 1892 511 "111111111"]
[4.665037870 19094 4093 "111111111101"]
[4.713727406 19298 4094 "111111111110"]
[4.898412698 20059 4095 "111111111111"]
[5.167124458 84653 16383 "11111111111111"]
[5.327494125 174566 32767 "111111111111111"]
[6.439611205 1688099 262143 "111111111111111111"]
The values of k and c(k) form the present sequence and A352920.

Cf. A109812, A113233, A352203, A352204, A352336, A352359, A352917-A352923.

A352921 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives p(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 7, 9, 9, 11, 12, 13, 13, 15, 15, 17, 17, 19

Offset: 1

David Broadhurst, Aug 17 2022 (entry created by N. J. A. Sloane, Apr 24 2022)

The sequences m, p, r are well-defined since every number appears in A109812, and if A109812(s) = 2^n - 1, then by definition both A109812(s-1) and A109812(s+1) must be multiples of 2^n.

The sequences m, p, r are discussed in A352920.

Cf. A109812, A113233, A352203, A352204, A352336, A352359, A352917-A352923.

cp's OEIS Frontend

A352923 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives r(n).

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A352922 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives m(n).

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A352919 Indices k where k/A109812(k) reaches a new high point.

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A352921 Let c(s) denote A109812(s). Suppose c(s) = 2^n - 1, and define m(n), p(n), r(n) by m(n) = c(s-1)/2^n, p(n) = c(s+1)/2^n, r(n) = max(m(n), p(n)); sequence gives p(n).

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