A295566 -id:A295566 - cp's OEIS frontend

A295567 Consider numbers k such that A295563(k) > k (see A295566); sequence lists the values A295563(k).

2, 5, 9, 10, 12, 13, 17, 19, 18, 23, 25, 22, 24, 28, 34, 30, 37, 39, 36, 38, 40, 42, 41, 46, 45, 44, 51, 50, 57, 52, 59, 49, 55, 61, 63, 62, 66, 65, 67, 72, 71, 58, 73, 76, 75, 69, 70, 86, 82, 83, 88, 87, 91, 90, 97, 92, 95, 99, 105, 104, 93, 102, 108, 98, 106, 112, 110, 111, 109, 116, 121, 117, 114

Offset: 1

N. J. A. Sloane, Nov 29 2017

nonn

Do the ratios A295567(k)/A295566(k) converge and if so what is the limit?

Rémy Sigrist, Table of n, a(n) for n = 1..50000

Cf. A269526, A274528, A295563, A295564, A295565, A295566,

A295563 First row of array in A274528.

Original entry on oeis.org

0, 2, 1, 5, 3, 4, 9, 10, 12, 7, 13, 17, 6, 19, 18, 8, 11, 23, 25, 22, 24, 28, 15, 14, 34, 30, 37, 39, 36, 38, 40, 16, 42, 41, 46, 45, 44, 51, 26, 20, 21, 50, 57, 52, 59, 49, 55, 61, 63, 62, 66, 65, 67, 72, 71, 58, 73, 27, 76, 75, 69, 70, 29, 86, 31, 82, 83, 32, 33, 88, 87, 91, 90, 35, 97, 92, 95

Offset: 0

N. J. A. Sloane, Nov 29 2017

nonn

Note this is not a list, this gives the Grundy-value at (0,n) of the Lonely Queens array A274528 regarded as a game.
It would be nice to have a formula or recurrence.  Note that the first row of the analogous array corresponding to the Wythoff game, A004482, does have a simple formula.
The points seem to fall on or close to two lines, of slopes about 0.48 and 1.29 (what are these slopes?). See A295564, A295565, A295566, A295567 for the X- and Y-coordinates of the points on the two lines.

Rémy Sigrist, Table of n, a(n) for n = 0..99999 (terms 0..1999 from N. J. A. Sloane)
Rémy Sigrist, PARI program for A295563

Cf. A004482, A269526, A274528, A295564, A295565, A295566, A295567.

Equals A274315 - 1.

PARI
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See Links section.
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A295564 Numbers k such that A295563(k) <= k.

Original entry on oeis.org

0, 2, 4, 5, 9, 12, 15, 16, 22, 23, 31, 38, 39, 40, 57, 62, 64, 67, 68, 73, 90, 99, 101, 107, 110, 117, 126, 133, 143, 155, 160, 162, 165, 166, 171, 175, 177, 182, 194, 198, 207, 208, 213, 224, 236, 241, 245, 246, 248, 260, 261, 265, 266, 285, 291, 293, 297, 298, 304, 311, 328, 329, 332, 337, 338, 341

Offset: 1

N. J. A. Sloane, Nov 29 2017

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..15000

Cf. A269526, A274528, A295563, A295565, A295566, A295567,

A295565 Consider numbers k such that A295563(k) <= k (see A295564); sequence lists the values A295563(k).

Original entry on oeis.org

0, 1, 3, 4, 7, 6, 8, 11, 15, 14, 16, 26, 20, 21, 27, 29, 31, 32, 33, 35, 43, 47, 48, 54, 53, 56, 60, 64, 68, 74, 77, 78, 80, 79, 81, 84, 85, 89, 94, 96, 101, 100, 103, 107, 113, 115, 118, 119, 120, 126, 127, 128, 129, 139, 141, 142, 143, 144, 147, 151, 158, 160, 159, 164, 163, 167, 165, 175, 177, 180

Offset: 1

N. J. A. Sloane, Nov 29 2017

nonn

Do the ratios A295565(k)/A295564(k) converge and if so what is the limit?

Rémy Sigrist, Table of n, a(n) for n = 1..15000

Cf. A269526, A274528, A295563, A295564, A295566, A295567,

cp's OEIS Frontend

A295567 Consider numbers k such that A295563(k) > k (see A295566); sequence lists the values A295563(k).

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A295563 First row of array in A274528.

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PARI

A295564 Numbers k such that A295563(k) <= k.

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A295565 Consider numbers k such that A295563(k) <= k (see A295564); sequence lists the values A295563(k).

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