A035403 -id:A035403 - cp's OEIS frontend

A035413 First differences of A035403.

4, 4, 20, 5, 8, 23, 6, 6, 5, 12, 100, 5, 13, 3, 7, 14, 4, 10, 19, 102, 6, 7, 5, 28, 4, 4, 10, 25, 7, 14, 24, 409, 5, 13, 3, 7, 19, 4, 4, 10, 69, 5, 13, 8, 16, 48, 5, 12, 21, 33, 386, 6, 7, 5, 30, 4, 4, 10, 31, 6, 4, 9, 7, 14, 118, 5, 8, 19, 5, 12, 21, 73, 8

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Cf. A003114, A035403, A035411, A035412, A035414, A035415.

New name from Andrey Zabolotskiy, Mar 26 2025

Revised by Geoffrey Caveney and Sean A. Irvine, Sep 03 2025

A035401 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 1 (mod 5).

Original entry on oeis.org

1, 4, 14, 19, 32, 37, 45, 99, 105, 109, 118, 125, 139, 197, 202, 215, 218, 225, 239, 243, 253, 272, 510, 516, 520, 528, 531, 538, 577, 583, 588, 600, 633, 641, 657, 684, 917, 922, 935, 938, 945, 964, 968, 972, 982, 1051, 1056, 1069, 1077, 1093, 1141, 1146

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Sean A. Irvine, Table of n, a(n) for n = 1..1000
Sean A. Irvine, Java program (github)
N. J. A. Sloane, An exchange of emails with Olivier Gerard concerning this sequence

Cf. A003114, A035402, A035403, A035404, A035405.

Revised by Geoffrey Caveney and Sean A. Irvine, Sep 03 2025

A035402 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 2 (mod 5).

Original entry on oeis.org

2, 7, 20, 23, 30, 49, 53, 57, 67, 140, 143, 153, 158, 171, 179, 195, 276, 280, 284, 303, 308, 316, 335, 340, 352, 373, 685, 688, 698, 703, 716, 721, 729, 780, 784, 793, 800, 814, 852, 856, 866, 885, 915, 1216, 1220, 1224, 1244, 1249, 1257, 1280, 1286, 1292

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A003114, A035401, A035403, A035404, A035405.

Revised by Geoffrey Caveney and Sean A. Irvine, Sep 03 2025

A035404 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 4 (mod 5).

Original entry on oeis.org

1, 7, 14, 19, 49, 53, 57, 67, 99, 105, 109, 118, 125, 139, 276, 280, 284, 303, 308, 316, 335, 340, 352, 373, 510, 516, 520, 528, 531, 538, 577, 583, 588, 600, 633, 641, 657, 684, 1216, 1220, 1224, 1244, 1249, 1257, 1280, 1286, 1292, 1297, 1309, 1399, 1402

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A003114, A035401, A035402, A035403, A035405.

Revised by Geoffrey Caveney and Sean A. Irvine, Sep 03 2025

A035405 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 0 (mod 5).

Original entry on oeis.org

2, 8, 12, 20, 23, 30, 68, 74, 80, 85, 97, 140, 143, 153, 158, 171, 179, 195, 374, 380, 387, 392, 420, 424, 428, 438, 463, 470, 484, 508, 685, 688, 698, 703, 716, 721, 729, 780, 784, 793, 800, 814, 852, 856, 866, 885, 915, 1598, 1604, 1611, 1616, 1646, 1650

Offset: 1

Olivier Gérard

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A003114, A035401, A035402, A035403, A035404.

Revised by Geoffrey Caveney and Sean A. Irvine, Sep 03 2025

cp's OEIS Frontend

A035413 First differences of A035403.

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A035401 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 1 (mod 5).

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A035402 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 2 (mod 5).

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A035404 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 4 (mod 5).

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A035405 Limit of the position of the n-th partition into parts 5k+1 or 5k+4 in the list of all integer partitions sorted in reverse lexicographic order, for integers == 0 (mod 5).

Views

Author

Keywords

References

Links

Crossrefs

Extensions