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 1-6 of 6 results.

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])

A345551 Numbers that are the sum of ten cubes in three or more ways.

Original entry on oeis.org

197, 225, 232, 239, 246, 251, 253, 258, 260, 265, 267, 272, 277, 279, 281, 284, 286, 288, 291, 293, 295, 298, 300, 302, 303, 305, 307, 309, 310, 312, 314, 316, 317, 319, 321, 323, 324, 326, 328, 329, 330, 335, 336, 338, 340, 342, 343, 344, 345, 347, 349, 351
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			225 is a term because 225 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 5^3 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 4^3 = 1^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.

Links

Crossrefs

Cf. A345510, A345542, A345550, A345552, A345596, A345805.

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, 10):
    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])

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])

A345597 Numbers that are the sum of ten fourth powers in four or more ways.

Original entry on oeis.org

1620, 2660, 2725, 2740, 2835, 2855, 2870, 2900, 2915, 2920, 2935, 2950, 2965, 2980, 3000, 3015, 3030, 3045, 3095, 3110, 3160, 3175, 3190, 3205, 3220, 3240, 3255, 3270, 3285, 3335, 3350, 3415, 3430, 3445, 3460, 3479, 3510, 3525, 3544, 3559, 3574, 3589, 3639
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			2660 is a term because 2660 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4.

Links

Crossrefs

Cf. A345552, A345588, A345596, A345598, A345636, A345856.

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 >= 4])
    for x in range(len(rets)):
        print(rets[x])

A345855 Numbers that are the sum of ten fourth powers in exactly three ways.

Original entry on oeis.org

520, 535, 550, 600, 615, 680, 775, 790, 855, 1030, 1144, 1159, 1224, 1365, 1380, 1399, 1445, 1540, 1555, 1605, 1635, 1685, 1700, 1768, 1795, 1815, 1830, 1860, 1875, 1895, 1989, 2070, 2164, 2229, 2244, 2439, 2485, 2580, 2595, 2645, 2675, 2680, 2695, 2710, 2755
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345596 at term 21 because 1620 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4.

Examples

			535 is a term because 535 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 1^4 + 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A345596, A345805, A345845, A345854, A345856, A346348.

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 == 3])
    for x in range(len(rets)):
        print(rets[x])

A345635 Numbers that are the sum of ten fifth powers in three or more ways.

Original entry on oeis.org

8194, 21940, 52419, 52450, 52481, 52661, 52692, 52903, 53442, 53473, 53684, 54465, 54520, 54551, 54582, 54762, 54793, 55004, 55543, 55574, 55691, 55722, 55785, 55933, 56566, 56714, 57644, 57675, 57886, 58667, 58815, 60194, 60225, 60436, 60768, 61217, 62295
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			21940 is a term because 21940 = 1^5 + 2^5 + 2^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 + 5^5 = 1^5 + 3^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5.

Links

Crossrefs

Cf. A345596, A345620, A345634, A345636, A346348.

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, 10):
    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 1-6 of 6 results.

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