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 1-5 of 5 results.

A345820 Numbers that are the sum of six fourth powers in exactly eight ways.

Original entry on oeis.org

58035, 59780, 87746, 96195, 96450, 102371, 106451, 106515, 108035, 108275, 108290, 108771, 112370, 112931, 115251, 122835, 122850, 124691, 125971, 133395, 133571, 133586, 134675, 136931, 138275, 138595, 143650, 144755, 145826, 147491, 148820, 149571, 150115
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345565 at term 4 because 88595 = 1^4 + 4^4 + 5^4 + 12^4 + 13^4 + 14^4 = 1^4 + 6^4 + 6^4 + 11^4 + 12^4 + 15^4 = 1^4 + 7^4 + 8^4 + 9^4 + 10^4 + 16^4 = 2^4 + 8^4 + 9^4 + 9^4 + 12^4 + 15^4 = 2^4 + 10^4 + 11^4 + 11^4 + 12^4 + 13^4 = 4^4 + 6^4 + 6^4 + 9^4 + 13^4 + 15^4 = 5^4 + 6^4 + 7^4 + 8^4 + 11^4 + 16^4 = 7^4 + 7^4 + 10^4 + 11^4 + 12^4 + 14^4.

Examples

			59780 is a term because 59780 = 1^4 + 1^4 + 1^4 + 5^4 + 12^4 + 14^4 = 1^4 + 1^4 + 6^4 + 6^4 + 9^4 + 15^4 = 1^4 + 2^4 + 9^4 + 10^4 + 11^4 + 13^4 = 1^4 + 4^4 + 7^4 + 7^4 + 8^4 + 15^4 = 1^4 + 7^4 + 7^4 + 9^4 + 10^4 + 14^4 = 2^4 + 5^4 + 6^4 + 11^4 + 11^4 + 13^4 = 3^4 + 7^4 + 8^4 + 10^4 + 11^4 + 13^4 = 5^4 + 6^4 + 7^4 + 7^4 + 11^4 + 14^4.

Links

Crossrefs

Cf. A344945, A345565, A345770, A345819, A345821, A345830, A346363.

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 == 8])
    for x in range(len(rets)):
        print(rets[x])

A346285 Numbers that are the sum of seven fifth powers in exactly eight ways.

Original entry on oeis.org

36620574, 80552143, 81401376, 82078424, 92347417, 93653176, 94486699, 94626949, 98873875, 105674625, 121050874, 125959393, 129228307, 144209018, 145340799, 147245218, 147898763, 151727082, 151923168, 152361276, 152664876, 153877208, 155107349, 155270357
Offset: 1

Views

Author

David Consiglio, Jr., Jul 12 2021

Keywords

Comments

Differs from A345630 at term 11 because 110276376 = 1^5 + 3^5 + 5^5 + 7^5 + 17^5 + 23^5 + 40^5 = 5^5 + 10^5 + 16^5 + 16^5 + 19^5 + 20^5 + 40^5 = 1^5 + 8^5 + 14^5 + 16^5 + 21^5 + 27^5 + 39^5 = 7^5 + 8^5 + 11^5 + 14^5 + 16^5 + 33^5 + 37^5 = 4^5 + 7^5 + 8^5 + 13^5 + 26^5 + 31^5 + 37^5 = 1^5 + 5^5 + 6^5 + 20^5 + 28^5 + 29^5 + 37^5 = 3^5 + 3^5 + 7^5 + 18^5 + 27^5 + 32^5 + 36^5 = 6^5 + 12^5 + 18^5 + 25^5 + 30^5 + 31^5 + 34^5 = 6^5 + 10^5 + 20^5 + 27^5 + 27^5 + 33^5 + 33^5.

Examples

			36620574 is a term because 36620574 = 4^5 + 9^5 + 14^5 + 17^5 + 18^5 + 21^5 + 31^5 = 1^5 + 12^5 + 13^5 + 14^5 + 20^5 + 24^5 + 30^5 = 8^5 + 9^5 + 12^5 + 13^5 + 16^5 + 27^5 + 29^5 = 5^5 + 7^5 + 7^5 + 20^5 + 23^5 + 23^5 + 29^5 = 17^5 + 18^5 + 20^5 + 20^5 + 20^5 + 20^5 + 29^5 = 2^5 + 7^5 + 14^5 + 14^5 + 23^5 + 26^5 + 28^5 = 4^5 + 8^5 + 8^5 + 17^5 + 23^5 + 27^5 + 27^5 = 2^5 + 3^5 + 14^5 + 18^5 + 24^5 + 26^5 + 27^5.

Links

Crossrefs

Cf. A345630, A345830, A346284, A346286, A346333, A346363.

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, 7):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 8])
    for x in range(len(rets)):
        print(rets[x])

A345722 Numbers that are the sum of six fifth powers in eight or more ways.

Original entry on oeis.org

2295937600, 4335900525, 6251954544, 8986552608, 9085584992, 13413708308, 14539246326, 15277569450, 15728636000, 16770321920, 16873011232, 16933805856, 17572402769, 17713454592, 17960776999, 18190647200, 19621666592, 20570070125, 20827689300
Offset: 1

Views

Author

David Consiglio, Jr., Jun 24 2021

Keywords

Examples

			4335900525 is a term because 4335900525 = 2^5 + 24^5 + 34^5 + 56^5 + 61^5 + 78^5 = 3^5 + 21^5 + 37^5 + 54^5 + 62^5 + 78^5 = 3^5 + 21^5 + 39^5 + 49^5 + 66^5 + 77^5 = 3^5 + 26^5 + 32^5 + 49^5 + 72^5 + 73^5 = 8^5 + 16^5 + 42^5 + 49^5 + 61^5 + 79^5 = 9^5 + 13^5 + 43^5 + 47^5 + 66^5 + 77^5 = 19^5 + 20^5 + 30^5 + 45^5 + 61^5 + 80^5 = 21^5 + 24^5 + 28^5 + 37^5 + 67^5 + 78^5.

Links

Crossrefs

Cf. A345565, A345630, A345721, A345723, A346363.

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 >= 8])
    for x in range(len(rets)):
        print(rets[x])

A346362 Numbers that are the sum of six fifth powers in exactly seven ways.

Original entry on oeis.org

1184966816, 1700336000, 1717860100, 1972000800, 2229475325, 2396275200, 2548597632, 2625460992, 2886251808, 3217068800, 3697267200, 3729261536, 3765398725, 4046532448, 4165116967, 4246566632, 4286704224, 4489548050, 4539955200, 4623694108, 4710031469
Offset: 1

Views

Author

David Consiglio, Jr., Jul 13 2021

Keywords

Comments

Differs from A345721 at term 6 because 2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5 = 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5 = 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5 = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5 = 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5 = 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5 = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5 = 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5.

Examples

			1184966816 is a term because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.

Links

Crossrefs

Cf. A345721, A345819, A346284, A346361, A346363.

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 == 7])
    for x in range(len(rets)):
        print(rets[x])

A346364 Numbers that are the sum of six fifth powers in exactly nine ways.

Original entry on oeis.org

9085584992, 16933805856, 37377003050, 39254220544, 41066625600, 41485873792, 42149876800, 43828403850, 44180505600, 45902654525, 48588434400, 52005184992, 53536896864, 54156285568, 56229189632, 57088402525, 59954496800, 63432407850, 66188522400, 66507304800
Offset: 1

Views

Author

David Consiglio, Jr., Jul 13 2021

Keywords

Comments

This sequence differs from A345723:
55302546200 = 34^5 + 38^5 + 50^5 + 57^5 + 95^5 + 136^5
= 23^5 + 49^5 + 61^5 + 69^5 + 107^5 + 131^5
= 24^5 + 37^5 + 63^5 + 81^5 + 104^5 + 131^5
= 21^5 + 35^5 + 60^5 + 94^5 + 100^5 + 130^5
= 57^5 + 60^5 + 71^5 + 75^5 + 109^5 + 128^5
= 19^5 + 37^5 + 56^5 + 96^5 + 104^5 + 128^5
= 35^5 + 41^5 + 53^5 + 69^5 + 115^5 + 127^5
= 16^5 + 49^5 + 53^5 + 83^5 + 112^5 + 127^5
= 35^5 + 37^5 + 40^5 + 88^5 + 119^5 + 121^5
= 11^5 + 24^5 + 71^5 + 104^5 + 109^5 + 121^5,
so 55302546200 is in A345723, but is not in this sequence.

Examples

			9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
           = 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
           =  8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
           = 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
           = 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
           =  8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
           =  5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
           =  8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
           = 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
so 9085584992 is a term.

Links

Crossrefs

Cf. A345723, A345821, A346286, A346363, 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 == 9])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-5 of 5 results.

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