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.

A342687 Numbers that are the sum of five fifth powers in three or more ways.

Original entry on oeis.org

13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925
Offset: 1

Views

Author

David Consiglio, Jr., May 18 2021

Keywords

Links

Crossrefs

Cf. A342685, A342688, A344243, A344518, A345337, A345604.

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, 500)]
for pos in cwr(power_terms, 5):
    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])

A345863 Numbers that are the sum of five fifth powers in five or more ways.

Original entry on oeis.org

9006349824, 65799210368, 67629776576, 181085909632, 188189635424, 288203194368, 295677350451, 467139768468, 471359089024, 656243139157, 691381929281, 797466940832, 854533526901, 874953049024, 891862586132, 953769598750, 1038549256768
Offset: 1

Views

Author

David Consiglio, Jr., Jun 27 2021

Keywords

Links

Crossrefs

Cf. A344358, A344518, A345719, A345864, A346257.

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

A342688 Numbers that are the sum of five positive fifth powers in exactly three ways.

Original entry on oeis.org

13124675, 28055699, 50043937, 52679923, 53069024, 55097976, 57936559, 60484744, 62260463, 62445305, 70211956, 73133026, 79401728, 80368962, 84766210, 88512249, 93288865, 98824300, 106993391, 113055482, 117173891, 120968132, 123383875, 126416258, 131106051, 131529588, 132022925
Offset: 1

Views

Author

David Consiglio, Jr., May 18 2021

Keywords

Comments

Differs from A342687:
287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5
= 9^5 + 13^5 + 26^5 + 37^5 + 46^5
= 11^5 + 12^5 + 23^5 + 41^5 + 44^5
= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
So 287618651 is a term of A342687 but not a term of this sequence.
[Corrected by Patrick De Geest, Dec 28 2024]

Examples

			50043937 =  6^5 + 16^5 + 18^5 + 24^5 + 33^5
         =  7^5 + 13^5 + 21^5 + 23^5 + 33^5
         = 11^5 + 13^5 + 13^5 + 29^5 + 31^5
so 50043937 is a term of this sequence.
[Corrected by _Patrick De Geest_, Dec 28 2024]

Links

Crossrefs

Cf. A003350, A004845, A342685, A342686, A342687, A344244, A344519, A344518, A345863, A345864, A346257, A346358.

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, 500)]
for pos in cwr(power_terms, 5):
    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])

A344354 Numbers that are the sum of five fourth powers in four or more ways.

Original entry on oeis.org

20995, 21235, 31250, 41474, 43235, 43250, 43315, 43490, 43859, 45139, 46290, 47570, 51939, 53234, 53299, 54994, 56274, 57379, 57410, 57779, 59329, 59779, 63970, 67010, 67859, 68035, 68290, 71795, 71954, 73730, 73954, 75714, 75794, 77890, 82099, 84499, 86275, 86450, 87730, 92500, 93394, 93474, 93859
Offset: 1

Views

Author

David Consiglio, Jr., May 15 2021

Keywords

Examples

			31250 is a term of this sequence because 31250 = 2^4 + 2^4 + 4^4 + 7^4 + 13^4 = 2^4 + 3^4 + 6^4 + 6^4 + 13^4 = 4^4 + 6^4 + 7^4 + 9^4 + 12^4 = 5^4 + 5^4 + 10^4 + 10^4 + 10^4.

Links

Crossrefs

Cf. A344034, A344243, A344352, A344355, A344358, A344518, A345561.

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, 50)]
for pos in cwr(power_terms, 5):
    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])

A345718 Numbers that are the sum of six fifth powers in four or more ways.

Original entry on oeis.org

12047994, 20646208, 21017489, 21300963, 21741819, 24993485, 27669050, 28576064, 30193856, 30785920, 35480456, 35735194, 36082750, 37303264, 39035975, 46814942, 47963291, 50047062, 50724345, 52987561, 53076800, 53606848, 54827300, 55101101, 56766906
Offset: 1

Views

Author

David Consiglio, Jr., Jun 24 2021

Keywords

Examples

			20646208 is a term because 20646208 = 2^5 + 12^5 + 12^5 + 16^5 + 18^5 + 28^5 = 3^5 + 4^5 + 4^5 + 8^5 + 10^5 + 29^5 = 6^5 + 6^5 + 12^5 + 14^5 + 24^5 + 26^5 = 7^5 + 7^5 + 8^5 + 16^5 + 25^5 + 25^5.

Links

Crossrefs

Cf. A344518, A345561, A345604, A345607, A345719, A346359.

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

A344519 Numbers that are the sum of five positive fifth powers in exactly four ways.

Original entry on oeis.org

287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9051501568, 9203796832, 9254212901
Offset: 1

Views

Author

David Consiglio, Jr., May 21 2021

Keywords

Comments

Differs from A344518 at term 20 because
9006349824 = 8^5 + 34^5 + 62^5 + 68^5 + 92^5
= 8^5 + 41^5 + 47^5 + 79^5 + 89^5
= 12^5 + 18^5 + 72^5 + 78^5 + 84^5
= 21^5 + 34^5 + 43^5 + 74^5 + 92^5
= 24^5 + 42^5 + 48^5 + 54^5 + 96^5.

Examples

			287618651 is a term because
287618651 =  8^5 + 21^5 + 27^5 + 27^5 + 48^5
          =  9^5 + 13^5 + 26^5 + 37^5 + 46^5
          = 11^5 + 12^5 + 23^5 + 41^5 + 44^5
          = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
[Corrected by _Patrick De Geest_, Dec 28 2024]

Links

Crossrefs

Cf. A003350, A004845, A342685, A342686, A342687, A342688, A344244, A344355, A344518, A345863, A345864, A346257, A346358, A346359.

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, 500)]
for pos in cwr(power_terms, 5):
    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])
Showing 1-6 of 6 results.

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