A350393 -id:A350393 - cp's OEIS frontend

A350394 Largest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^k).

0, 1, 3, 3, 7, 10, 12, 16, 18, 24, 28, 33, 39, 46, 53, 60, 68, 77, 86, 95, 105, 116, 127, 138, 150, 163, 176, 189, 203, 218, 233, 248, 264, 281, 298, 315, 333, 352, 371, 390, 410, 431, 452, 473, 495, 518, 541, 564, 588, 613, 638, 663, 689, 716, 743, 770, 798, 827, 856, 885, 915, 946, 977

Offset: 0

Max Alekseyev, Dec 28 2021

nonn

Apparently, a(n) = A054925(n+1) for n >= 10. - Hugo Pfoertner, Dec 30 2021

Cf. A025591 (largest coefficient), A350393 (smallest degree of x), A350395, A350396.

Cf. A054925.

{ A350394(n) = my(v,t,x='x); v = Vec(prod(k=1,n,1+x^k)); vecmax(v,&t); #v-t; }

A350395 Numbers m such that a term with the largest coefficient in Product_{k=1..m} (1 + x^k) is unique.

Original entry on oeis.org

0, 3, 8, 11, 12, 15, 16, 19, 20, 23, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 100, 103, 104, 107, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127, 128, 131, 132, 135, 136, 139, 140, 143, 144, 147, 148, 151, 152, 155, 156, 159, 160, 163, 164, 167, 168, 171, 172, 175, 176, 179, 180, 183, 184, 187, 188, 191, 192, 195, 196

Offset: 1

Max Alekseyev, Dec 28 2021

nonn

Numbers m such that A350393(m) = A350394(m).

Apparently, a(n) = A014601(n+1) for n >= 3. - Hugo Pfoertner, Dec 30 2021

Complement of A350396.
Cf. A025591 (largest coefficient), A350393, A350394.
Cf. A014601.

A350396 Numbers m such that there are two or more terms with the largest coefficient in Product_{k=1..m} (1 + x^k).

Original entry on oeis.org

1, 2, 4, 5, 6, 7, 9, 10, 13, 14, 17, 18, 21, 22, 25, 26, 29, 30, 33, 34, 37, 38, 41, 42, 45, 46, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 97, 98, 101, 102, 105, 106, 109, 110, 113, 114, 117, 118, 121, 122, 125, 126, 129, 130, 133, 134, 137, 138, 141, 142, 145, 146, 149, 150, 153, 154, 157, 158, 161, 162, 165, 166, 169, 170, 173, 174, 177, 178

Offset: 1

Max Alekseyev, Dec 28 2021

nonn

Numbers m such that A350393(m) < A350394(m).

Apparently, a(n) = A042963(n-2) for n >= 7. - Hugo Pfoertner, Dec 30 2021

Complement of A350395.
Cf. A025591 (largest coefficient), A350393, A350394.
Cf. A042963.

A379563 Smallest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^prime(k)).

Original entry on oeis.org

0, 0, 0, 5, 5, 5, 18, 18, 35, 42, 58, 73, 89, 114, 137, 163, 190, 220, 249, 281, 318, 356, 393, 437, 480, 530, 580, 632, 685, 740, 796, 860, 925, 994, 1063, 1138, 1213, 1292, 1373, 1457, 1543, 1633, 1723, 1819, 1915, 2014, 2113, 2219, 2330, 2444, 2558, 2675, 2794, 2915, 3040, 3169

Offset: 0

Ilya Gutkovskiy, Dec 26 2024

nonn

Cf. A000586, A350393, A350457, A379564.

cp's OEIS Frontend

A350394 Largest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^k).

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A350395 Numbers m such that a term with the largest coefficient in Product_{k=1..m} (1 + x^k) is unique.

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Author

Keywords

Comments

Crossrefs

A350396 Numbers m such that there are two or more terms with the largest coefficient in Product_{k=1..m} (1 + x^k).

Views

Author

Keywords

Comments

Crossrefs

A379563 Smallest degree of x with the largest coefficient in Product_{k=1..n} (1 + x^prime(k)).

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Author

Keywords

Crossrefs