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.

A345512 Numbers that are the sum of six cubes in three or more ways.

Original entry on oeis.org

221, 254, 369, 411, 443, 469, 495, 502, 576, 595, 600, 626, 648, 658, 684, 704, 711, 720, 739, 746, 753, 760, 765, 767, 772, 774, 779, 786, 793, 811, 818, 828, 830, 835, 837, 844, 854, 856, 863, 866, 873, 874, 880, 884, 886, 891, 892, 893, 899, 905, 910, 919
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			254 is a term because 254 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

Links

Crossrefs

Cf. A048931, A343704, A344807, A345511, A345513, A345521, A345560.

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, 6):
    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])

A345522 Numbers that are the sum of seven cubes in four or more ways.

Original entry on oeis.org

470, 496, 503, 603, 627, 634, 653, 659, 685, 690, 692, 711, 712, 747, 751, 754, 761, 766, 768, 773, 775, 777, 780, 783, 787, 792, 794, 812, 813, 829, 831, 836, 838, 842, 843, 845, 857, 859, 864, 867, 871, 874, 875, 881, 883, 885, 890, 892, 894, 899, 900, 901
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			496 is a term because 496 = 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 6^3 = 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3.

Links

Crossrefs

Cf. A345481, A345513, A345521, A345523, A345534, A345570, A345776.

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, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 4])
    for x in range(len(rets)):
        print(rets[x])

A345533 Numbers that are the sum of eight cubes in three or more ways.

Original entry on oeis.org

223, 230, 237, 249, 256, 263, 270, 275, 282, 284, 286, 289, 291, 293, 308, 310, 312, 319, 326, 345, 347, 349, 354, 364, 371, 373, 375, 378, 380, 382, 385, 386, 387, 389, 397, 399, 401, 404, 406, 408, 410, 412, 413, 415, 420, 423, 427, 434, 438, 439, 441, 443
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			230 is a term because 230 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

Links

Crossrefs

Cf. A345490, A345521, A345532, A345534, A345542, A345578, A345785.

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, 8):
    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])

A345569 Numbers that are the sum of seven fourth powers in three or more ways.

Original entry on oeis.org

2677, 2692, 2757, 2852, 2867, 2917, 2932, 2997, 3107, 3172, 3301, 3476, 3541, 3972, 4132, 4147, 4212, 4227, 4242, 4257, 4307, 4322, 4372, 4387, 4437, 4452, 4482, 4497, 4562, 4627, 4737, 4756, 4851, 4866, 4867, 4931, 4996, 5077, 5106, 5107, 5122, 5187, 5252
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			2692 is a term because 2692 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.

Links

Crossrefs

Cf. A345521, A345560, A345568, A345570, A345578, A345606, A345825.

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, 7):
    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])

A345520 Numbers that are the sum of seven cubes in two or more ways.

Original entry on oeis.org

131, 159, 166, 173, 185, 192, 211, 222, 229, 236, 243, 248, 255, 257, 262, 264, 269, 274, 276, 281, 283, 285, 288, 290, 292, 295, 299, 300, 302, 307, 309, 311, 314, 318, 320, 321, 325, 332, 333, 337, 339, 340, 344, 346, 348, 351, 353, 355, 358, 359, 360, 363
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.

Links

Crossrefs

Cf. A003330, A345479, A345511, A345521, A345532, A345568, A345774.

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, 7):
    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])

A345775 Numbers that are the sum of seven cubes in exactly three ways.

Original entry on oeis.org

222, 229, 248, 255, 262, 281, 283, 285, 318, 346, 370, 374, 377, 379, 381, 396, 400, 407, 412, 419, 426, 433, 437, 438, 444, 451, 463, 472, 475, 477, 489, 494, 501, 505, 507, 510, 522, 529, 533, 536, 559, 564, 566, 568, 570, 577, 578, 584, 585, 592, 594, 596
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345521 at term 28 because 470 = 1^3 + 1^3 + 1^3 + 1^3 + 5^3 + 5^3 + 6^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 6^3 + 6^3 = 1^3 + 3^3 + 4^3 + 4^3 + 4^3 + 5^3 + 5^3 = 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 6^3.
Likely finite.

Examples

			229 is a term because 229 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 5^3 = 1^3 + 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3.

Links

Crossrefs

Cf. A048931, A345521, A345774, A345776, A345785, A345825.

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, 7):
    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])

A345480 Numbers that are the sum of seven squares in three or more ways.

Original entry on oeis.org

31, 34, 37, 39, 40, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			34 is a term because 34 = 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 5^2 = 1^2 + 1^2 + 1^2 + 2^2 + 3^2 + 3^2 + 3^2 = 1^2 + 1^2 + 2^2 + 2^2 + 2^2 + 2^2 + 4^2.

Links

Crossrefs

Cf. A344807, A345479, A345481, A345490, A345521.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**2 for x in range(1, 1000)]
for pos in cwr(power_terms, 7):
    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])
Showing 1-7 of 7 results.

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

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