cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A003343 Numbers that are the sum of 9 positive 4th powers.

Original entry on oeis.org

9, 24, 39, 54, 69, 84, 89, 99, 104, 114, 119, 129, 134, 144, 149, 164, 169, 179, 184, 194, 199, 209, 214, 229, 244, 249, 259, 264, 274, 279, 294, 309, 324, 329, 339, 344, 354, 359, 369, 374, 384, 389, 404, 409, 419, 424, 434, 439, 449, 454, 469, 484, 489, 499, 504
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 02 2020: (Start)
4644 is in the sequence as 4644 = 1^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4.
7541 is in the sequence as 7541 = 1^4 + 1^4 + 2^4 + 4^4 + 5^4 + 5^4 + 5^4 + 6^4 + 8^4.
10855 is in the sequence as 10855 = 1^4 + 3^4 + 3^4 + 5^4 + 5^4 + 5^4 + 5^4 + 8^4 + 8^4. (End)

Links

Crossrefs

Cf. A003332, A003342, A003344, A003354, A345586, A345843.

Programs

  • Mathematica
    Select[Range[500], AnyTrue[PowersRepresentations[#, 9, 4], First[#]>0&]&] (* Jean-François Alcover, Jul 18 2017 *)

A345577 Numbers that are the sum of eight fourth powers in two or more ways.

Original entry on oeis.org

263, 278, 293, 308, 323, 343, 358, 373, 388, 423, 438, 453, 503, 518, 533, 548, 563, 583, 598, 613, 628, 678, 693, 758, 773, 788, 803, 853, 868, 887, 902, 917, 932, 933, 967, 982, 997, 1028, 1043, 1047, 1062, 1108, 1127, 1142, 1157, 1172, 1222, 1237, 1283
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			278 is a term because 278 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A003342, A345532, A345568, A345578, A345586, A345610, A345834.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345587 Numbers that are the sum of nine fourth powers in three or more ways.

Original entry on oeis.org

519, 534, 599, 774, 1143, 1364, 1539, 1604, 1619, 1814, 2579, 2644, 2659, 2679, 2694, 2709, 2724, 2739, 2754, 2759, 2774, 2789, 2819, 2834, 2839, 2854, 2869, 2884, 2899, 2919, 2934, 2949, 2964, 2994, 2999, 3014, 3029, 3079, 3094, 3109, 3124, 3139, 3159, 3174
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			534 is a term because 534 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A345542, A345578, A345586, A345588, A345596, A345620, A345845.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345844 Numbers that are the sum of nine fourth powers in exactly two ways.

Original entry on oeis.org

264, 279, 294, 309, 324, 339, 344, 359, 374, 389, 404, 424, 439, 454, 469, 504, 549, 564, 579, 584, 614, 629, 644, 664, 679, 694, 709, 759, 789, 804, 819, 839, 854, 869, 884, 888, 903, 918, 933, 934, 948, 949, 968, 983, 998, 1013, 1014, 1029, 1044, 1048, 1059
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345586 at term 17 because 519 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

Examples

			279 is a term because 279 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A345586, A345794, A345834, A345843, A345845, A345854, A346337.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 2])
    for x in range(len(rets)):
        print(rets[x])

A345541 Numbers that are the sum of nine cubes in two or more ways.

Original entry on oeis.org

72, 133, 140, 147, 159, 161, 166, 168, 175, 182, 185, 187, 189, 194, 196, 198, 201, 203, 205, 208, 213, 217, 220, 222, 224, 227, 231, 238, 239, 243, 245, 246, 250, 252, 257, 259, 261, 264, 265, 266, 271, 273, 276, 278, 280, 283, 285, 287, 289, 290, 292, 294
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			133 is a term because 133 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3.

Links

Crossrefs

Cf. A003332, A345499, A345532, A345542, A345550, A345586, A345794.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345595 Numbers that are the sum of ten fourth powers in two or more ways.

Original entry on oeis.org

265, 280, 295, 310, 325, 340, 345, 355, 360, 375, 390, 405, 420, 425, 440, 455, 470, 485, 505, 520, 535, 550, 565, 580, 585, 595, 600, 615, 630, 645, 660, 665, 680, 695, 710, 725, 745, 760, 775, 790, 805, 820, 835, 840, 855, 870, 885, 889, 900, 904, 919, 920
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			280 is a term because 280 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A003344, A345550, A345586, A345596, A345634, A345854.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 1000)]
for pos in cwr(power_terms, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345619 Numbers that are the sum of nine fifth powers in two or more ways.

Original entry on oeis.org

4101, 4132, 4163, 4194, 4225, 4343, 4374, 4405, 4436, 4585, 4616, 4647, 4827, 4858, 5069, 5124, 5155, 5186, 5217, 5366, 5397, 5428, 5608, 5639, 5850, 6147, 6178, 6209, 6389, 6420, 6631, 7170, 7201, 7225, 7256, 7287, 7318, 7412, 7467, 7498, 7529, 7709, 7740
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			4132 is a term because 4132 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

Links

Crossrefs

Cf. A003354, A345586, A345610, A345620, A345634, A346337.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**5 for x in range(1, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 2])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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