A379060 -id:A379060 - cp's OEIS frontend

A379063 a(n) = min{A379059(n), A379060(n)}.

0, 1, 2, 5, 6, 7, 10, 11, 12, 17, 18, 19, 20, 21, 27, 28, 29, 30, 31, 37, 38, 39, 40, 41, 42, 43, 49, 50, 51, 57, 58, 59, 60, 65, 66, 67, 68, 69, 70, 71, 72, 73, 82, 83, 84, 85, 86, 87, 88, 89, 90, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 144, 145, 146, 151, 152, 153, 154, 155, 156, 157, 158, 159

Offset: 0

N. J. A. Sloane, Dec 27 2024

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..9940

Cf. A377091, A379059, A379060, A379064, A379065.

A379064 a(n) = max{A379059(n), A379060(n)}.

Original entry on oeis.org

0, 4, 3, 9, 8, 16, 15, 14, 13, 22, 23, 24, 25, 26, 33, 34, 35, 36, 32, 46, 45, 44, 48, 47, 52, 53, 54, 55, 56, 64, 63, 62, 61, 78, 77, 76, 75, 79, 80, 81, 74, 92, 93, 94, 95, 96, 97, 98, 99, 100, 91, 113, 114, 115, 116, 117, 118, 119, 120, 121, 112, 136, 135, 134, 138, 137, 141, 140, 139, 143, 142, 147, 133, 148, 149, 150, 163, 164, 165, 166, 162, 169, 168, 167, 161, 170

Offset: 0

N. J. A. Sloane, Dec 27 2024

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..9940

Cf. A377091, A379059, A379060, A379063, A379065.

A379787 a(n) = A379060(n) - 2*n.

Original entry on oeis.org

0, 2, -1, 3, 0, 6, 3, 0, -3, -1, -2, -3, -4, 0, -1, -2, -3, -4, -5, -1, -2, -3, -4, -5, -6, 3, 2, 1, 0, -1, -2, -3, -4, 12, 9, 6, 3, 5, 4, 3, -6, 10, 9, 8, 7, 6, 5, 4, 3, 2, -9, 11, 10, 9, 8, 7, 6, 5, 4, 3, -8, 14, 11, 8, 10, 7, 9, 6, 3, 5, 2, 5, -11, -2, -3, -4, 11, 10, 9, 8, 2, 7, 4, 1, -7, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11

Offset: 0

N. J. A. Sloane, Jan 13 2025

sign

N. J. A. Sloane, Table of n, a(n) for n = 0..9940

Cf. A377901, A379059, A379060, A379786.

A379059 Index of n in A377091, or -1 if n does not appear there.

Original entry on oeis.org

0, 1, 2, 5, 6, 7, 10, 11, 12, 22, 23, 24, 25, 21, 33, 34, 35, 36, 32, 46, 45, 44, 48, 47, 52, 43, 49, 50, 51, 64, 63, 62, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 82, 83, 84, 85, 86, 87, 88, 89, 90, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 188

Offset: 0

N. J. A. Sloane, Dec 26 2024

nonn

It is conjectured that every integer appears in A377091.
Conjecture 1: For n >= 10, |a(n) - 2*n| < 2*sqrt(n); for n >= 1000, |a(n) - 2*n| < 1.59*sqrt(n) (compare A379786). - N. J. A. Sloane, Jan 19 2025
Conjecture 2: lim sup |a(n) - 2*n|/sqrt(n) = sqrt(2) as n -> oo. - N. J. A. Sloane and Paolo Xausa, Feb 02 2025

N. J. A. Sloane, Table of n, a(n) for n = 0..10000
Paolo Xausa, Scatterplot of |a(n) - 2*n| for n <= 100000. The orange line is sqrt(2*n).

Cf. A377091, A379060, A379786.

A379786 a(n) = A379059(n) - 2*n.

Original entry on oeis.org

0, -1, -2, -1, -2, -3, -2, -3, -4, 4, 3, 2, 1, -5, 5, 4, 3, 2, -4, 8, 5, 2, 4, 1, 4, -7, -3, -4, -5, 6, 3, 0, -3, -1, -2, -3, -4, -5, -6, -7, -8, -9, -2, -3, -4, -5, -6, -7, -8, -9, -10, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, 16, 13

Offset: 0

N. J. A. Sloane, Jan 13 2025

sign

Conjecture: For n >= 10, |a(n)| < 2*sqrt(n); for n >= 1000, |a(n)| < 1.59*sqrt(n). - N. J. A. Sloane, Jan 19 2025

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Cf. A377901, A379059, A379060, A379787.

A379065 a(n) = A379064(n) - A379063(n).

Original entry on oeis.org

0, 3, 1, 4, 2, 9, 5, 3, 1, 5, 5, 5, 5, 5, 6, 6, 6, 6, 1, 9, 7, 5, 8, 6, 10, 10, 5, 5, 5, 7, 5, 3, 1, 13, 11, 9, 7, 10, 10, 10, 2, 19, 11, 11, 11, 11, 11, 11, 11, 11, 1, 12, 12, 12, 12, 12, 12, 12, 12, 12, 2, 25, 13, 11, 14, 12, 15, 13, 11, 14, 12, 16, 1, 4, 4, 4, 12, 12, 12, 12, 7, 13, 11, 9, 2, 10, 17, 15, 13, 11, 14, 14, 14, 14, 14, 14, 14, 14, 1, 17, 15, 18, 16, 14, 10

Offset: 0

N. J. A. Sloane, Dec 27 2024

nonn

This is the number of steps between the appearances of n and -n in A377091.

N. J. A. Sloane, Table of n, a(n) for n = 0..9940

Cf. A377091, A379059, A379060, A379063, A379064.

A379069 Nonnegative numbers k such that the index of -k in A377091 is <= the index of k.

Original entry on oeis.org

0, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 73, 74, 75, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 146, 147, 148

Offset: 1

N. J. A. Sloane, Dec 28 2024

nonn

Numbers k >= 0 such that A379060(k) <= A379059(k).

N. J. A. Sloane, Table of n, a(n) for n = 1..5837

Cf. A377091, A379059, A379060.

cp's OEIS Frontend

A379063 a(n) = min{A379059(n), A379060(n)}.

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A379064 a(n) = max{A379059(n), A379060(n)}.

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A379787 a(n) = A379060(n) - 2*n.

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A379059 Index of n in A377091, or -1 if n does not appear there.

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A379786 a(n) = A379059(n) - 2*n.

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A379065 a(n) = A379064(n) - A379063(n).

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A379069 Nonnegative numbers k such that the index of -k in A377091 is <= the index of k.

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