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.

A345566 Numbers that are the sum of six fourth powers in nine or more ways.

Original entry on oeis.org

88595, 122915, 132546, 134931, 144835, 146450, 151556, 161475, 162355, 162755, 170275, 171555, 171795, 172036, 172835, 173075, 177380, 177716, 180770, 183540, 183620, 184835, 185315, 185555, 187700, 187715, 190100, 190211, 193635, 195380, 195780, 196435
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			122915 is a term because 122915 = 1^4 + 3^4 + 6^4 + 9^4 + 10^4 + 18^4 = 1^4 + 4^4 + 7^4 + 8^4 + 15^4 + 16^4 = 1^4 + 7^4 + 9^4 + 10^4 + 14^4 + 16^4 = 2^4 + 3^4 + 4^4 + 5^4 + 14^4 + 17^4 = 2^4 + 4^4 + 5^4 + 7^4 + 11^4 + 18^4 = 2^4 + 9^4 + 9^4 + 12^4 + 14^4 + 15^4 = 3^4 + 5^4 + 6^4 + 6^4 + 11^4 + 18^4 = 3^4 + 8^4 + 10^4 + 11^4 + 13^4 + 16^4 = 5^4 + 6^4 + 7^4 + 11^4 + 14^4 + 16^4 = 8^4 + 8^4 + 9^4 + 10^4 + 11^4 + 17^4.

Links

Crossrefs

Cf. A341891, A345518, A345565, A345567, A345575, A345723, A345821.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])

A345519 Numbers that are the sum of six cubes in ten or more ways.

Original entry on oeis.org

3104, 3215, 3222, 3267, 3313, 3339, 3374, 3430, 3465, 3491, 3493, 3528, 3547, 3584, 3645, 3654, 3698, 3708, 3736, 3745, 3752, 3754, 3761, 3771, 3780, 3789, 3817, 3824, 3843, 3862, 3869, 3878, 3880, 3888, 3906, 3915, 3923, 3943, 3950, 3969, 3995, 4004, 4014
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			3215 is a term because 3215 = 1^3 + 1^3 + 1^3 + 4^3 + 6^3 + 13^3 = 1^3 + 1^3 + 2^3 + 2^3 + 9^3 + 12^3 = 1^3 + 1^3 + 3^3 + 8^3 + 8^3 + 11^3 = 1^3 + 2^3 + 3^3 + 5^3 + 8^3 + 12^3 = 1^3 + 3^3 + 3^3 + 3^3 + 10^3 + 11^3 = 1^3 + 3^3 + 8^3 + 8^3 + 8^3 + 9^3 = 2^3 + 3^3 + 6^3 + 6^3 + 8^3 + 11^3 = 3^3 + 3^3 + 3^3 + 8^3 + 9^3 + 10^3 = 3^3 + 5^3 + 5^3 + 5^3 + 6^3 + 12^3 = 6^3 + 6^3 + 6^3 + 6^3 + 7^3 + 10^3.

Links

Crossrefs

Cf. A345187, A345477, A345506, A345518, A345567, A345772.

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 >= 10])
    for x in range(len(rets)):
        print(rets[x])

A345576 Numbers that are the sum of seven fourth powers in ten or more ways.

Original entry on oeis.org

31251, 44547, 45827, 45892, 45907, 47667, 47971, 48292, 49572, 49812, 50052, 51092, 52372, 53316, 53476, 54531, 54596, 54756, 54996, 57411, 58036, 58116, 58276, 58516, 58660, 58756, 59331, 59781, 59796, 59811, 59827, 59861, 59876, 59892, 60036, 60371, 60436
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			44547 is a term because 44547 = 1^4 + 2^4 + 2^4 + 2^4 + 6^4 + 11^4 + 13^4 = 1^4 + 2^4 + 2^4 + 6^4 + 7^4 + 7^4 + 14^4 = 1^4 + 2^4 + 6^4 + 6^4 + 9^4 + 11^4 + 12^4 = 1^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4 + 13^4 = 2^4 + 2^4 + 8^4 + 9^4 + 9^4 + 9^4 + 12^4 = 2^4 + 4^4 + 6^4 + 6^4 + 9^4 + 9^4 + 13^4 = 2^4 + 4^4 + 7^4 + 7^4 + 8^4 + 11^4 + 12^4 = 3^4 + 3^4 + 4^4 + 4^4 + 7^4 + 12^4 + 12^4 = 3^4 + 6^4 + 6^4 + 7^4 + 8^4 + 11^4 + 12^4 = 4^4 + 4^4 + 8^4 + 8^4 + 9^4 + 11^4 + 11^4.

Links

Crossrefs

Cf. A345506, A345567, A345575, A345585, A345643, A345832.

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 >= 10])
    for x in range(len(rets)):
        print(rets[x])

A345822 Numbers that are the sum of six fourth powers in exactly ten ways.

Original entry on oeis.org

122915, 151556, 161475, 162755, 173075, 183620, 185315, 199106, 199940, 201875, 202275, 204275, 204340, 204595, 206115, 207395, 209795, 211075, 213731, 217826, 217891, 218515, 221250, 223955, 224180, 225875, 226595, 227186, 228035, 236195, 237796, 237890
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345567 at term 8 because 197795 = 1^4 + 2^4 + 5^4 + 6^4 + 16^4 + 19^4 = 1^4 + 2^4 + 7^4 + 11^4 + 12^4 + 20^4 = 1^4 + 2^4 + 10^4 + 12^4 + 17^4 + 17^4 = 2^4 + 4^4 + 7^4 + 9^4 + 13^4 + 20^4 = 2^4 + 11^4 + 13^4 + 14^4 + 15^4 + 16^4 = 3^4 + 6^4 + 6^4 + 9^4 + 13^4 + 20^4 = 3^4 + 6^4 + 7^4 + 14^4 + 15^4 + 18^4 = 4^4 + 9^4 + 11^4 + 12^4 + 15^4 + 18^4 = 7^4 + 7^4 + 14^4 + 14^4 + 15^4 + 16^4.

Examples

			151556 is a term because 151556 = 1^4 + 2^4 + 2^4 + 9^4 + 11^4 + 19^4 = 1^4 + 2^4 + 3^4 + 7^4 + 16^4 + 17^4 = 1^4 + 8^4 + 11^4 + 12^4 + 13^4 + 17^4 = 2^4 + 3^4 + 7^4 + 8^4 + 11^4 + 19^4 = 3^4 + 3^4 + 3^4 + 4^4 + 12^4 + 19^4 = 3^4 + 4^4 + 11^4 + 11^4 + 14^4 + 17^4 = 3^4 + 4^4 + 13^4 + 13^4 + 13^4 + 16^4 = 4^4 + 6^4 + 9^4 + 9^4 + 9^4 + 19^4 = 4^4 + 7^4 + 11^4 + 11^4 + 11^4 + 18^4 = 4^4 + 8^4 + 9^4 + 13^4 + 13^4 + 17^4.

Links

Crossrefs

Cf. A341898, A345567, A345772, A345821, A345832, A346365.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 10])
    for x in range(len(rets)):
        print(rets[x])

A341897 Numbers that are the sum of five fourth powers in ten or more ways.

Original entry on oeis.org

954979, 1205539, 1574850, 1713859, 1801459, 1863859, 1877394, 1882579, 2071939, 2109730, 2138419, 2142594, 2157874, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2663539, 2711394, 2784499, 2835939, 2847394, 2849859, 2880994, 2919154, 2924674, 3007474
Offset: 1

Views

Author

David Consiglio, Jr., Jun 04 2021

Keywords

Examples

			954979 =  1^4 +  2^4 + 11^4 + 19^4 + 30^4
       =  1^4 +  7^4 + 18^4 + 25^4 + 26^4
       =  3^4 +  8^4 + 17^4 + 20^4 + 29^4
       =  4^4 +  8^4 + 13^4 + 25^4 + 27^4
       =  4^4 +  9^4 + 10^4 + 11^4 + 31^4
       =  6^4 +  6^4 + 15^4 + 21^4 + 29^4
       =  7^4 + 10^4 + 18^4 + 19^4 + 29^4
       = 11^4 + 11^4 + 20^4 + 22^4 + 27^4
       = 16^4 + 17^4 + 17^4 + 24^4 + 25^4
       = 18^4 + 19^4 + 20^4 + 23^4 + 23^4
so 954979 is a term.

Links

Crossrefs

Cf. A341891, A341898, A344928, A345187, A345567.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v >= 10])
for x in range(len(rets)):
    print(rets[x])

A344196 Numbers that are the sum of six fifth powers in ten or more ways.

Original entry on oeis.org

55302546200, 89999127392, 96110537743, 104484239200, 120492759200, 121258798144, 127794946400, 133364991375, 135030535200, 136156575744, 151305014432, 155434423925, 174388570400, 177099008000, 179272687000, 180336745600, 182844944832, 184948721056, 187873845500
Offset: 1

Views

Author

David Consiglio, Jr., Jun 25 2021

Keywords

Examples

			89999127392 =  4^5 + 36^5 + 39^5 +  40^5 +  90^5 + 153^5
            =  8^5 + 21^5 + 90^5 + 109^5 + 119^5 + 135^5
            =  8^5 + 28^5 + 98^5 + 102^5 + 104^5 + 142^5
            = 10^5 + 38^5 + 74^5 + 102^5 + 118^5 + 140^5
            = 13^5 + 51^5 + 64^5 +  98^5 + 112^5 + 144^5
            = 18^5 + 44^5 + 66^5 +  98^5 + 112^5 + 144^5
            = 18^5 + 52^5 + 72^5 +  78^5 + 118^5 + 144^5
            = 28^5 + 60^5 + 63^5 +  65^5 + 124^5 + 142^5
            = 36^5 + 53^5 + 62^5 +  63^5 + 129^5 + 139^5
            = 39^5 + 41^5 + 64^5 +  91^5 +  98^5 + 149^5
so 89999127392 is a term.

Links

Crossrefs

Cf. A345567, A345643, A345723, A346365.

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, 6):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 10])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-6 of 6 results.

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