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 1-9 of 9 results.

A003350 Numbers that are the sum of 5 positive 5th powers.

Original entry on oeis.org

5, 36, 67, 98, 129, 160, 247, 278, 309, 340, 371, 489, 520, 551, 582, 731, 762, 793, 973, 1004, 1028, 1059, 1090, 1121, 1152, 1215, 1270, 1301, 1332, 1363, 1512, 1543, 1574, 1754, 1785, 1996, 2051, 2082, 2113, 2144, 2293, 2324, 2355, 2535, 2566, 2777, 3074, 3105, 3129
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 03 2020: (Start)
122490 is in the sequence as 122490 = 3^5 + 4^5 + 5^5 + 9^5 + 9^5.
251124 is in the sequence as 251124 = 1^5 + 3^5 + 4^5 + 4^5 + 12^5.
349858 is in the sequence as 349858 = 1^5 + 1^5 + 4^5 + 10^5 + 12^5. (End)

Links

Crossrefs

Cf. A000584, A003349, A003351, A003339, A342685, A344643
Column k=5 of A336725.

Programs

  • Mathematica
    f[upto_]:=Module[{max=Floor[Power[upto, (5)^-1]],tp},tp=Union[ Total/@ (Tuples[ Range[max],{5}]^5)]; Select[tp,#<=upto&]]; f[2100]  (* Harvey P. Dale, Mar 22 2011 *)

A342686 Numbers that are the sum of five fifth powers in exactly two ways.

Original entry on oeis.org

4097, 51446, 51477, 51688, 52469, 54570, 59221, 68252, 68905, 84213, 110494, 131104, 151445, 212496, 300277, 325174, 325713, 355114, 422135, 422738, 589269, 637418, 794434, 810820, 876734, 876765, 876976, 877757, 879858, 884509, 893540, 909501, 924912, 935782, 976733, 995571, 1037784, 1083457
Offset: 1

Views

Author

David Consiglio, Jr., May 18 2021

Keywords

Comments

This sequence differs from A342685:
13124675 = 1^5 + 9^5 + 10^5 + 20^5 + 25^5
= 2^5 + 5^5 + 12^5 + 23^5 + 23^5
= 16^5 + 19^5 + 20^5 + 20^5 + 20^5,
so 13124675 is in A342685, but is not in this sequence.

Examples

			51477 = 2^5 + 4^5 + 7^5 + 7^5 + 7^5
      = 2^5 + 5^5 + 6^5 + 6^5 + 8^5
so 51477 is a term of this sequence.

Links

Crossrefs

Cf. A342685, A342688, A344237, A344643, A344645, A346357.

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 == 2])
for x in range(len(rets)):
    print(rets[x])

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])

A344238 Numbers that are the sum of five fourth powers in two or more ways.

Original entry on oeis.org

260, 275, 340, 515, 884, 1555, 2595, 2660, 2675, 2690, 2705, 2755, 2770, 2835, 2930, 2945, 3010, 3185, 3299, 3314, 3379, 3554, 3923, 3970, 3985, 4050, 4115, 4145, 4160, 4210, 4225, 4290, 4355, 4400, 4465, 4594, 4769, 4834, 5075, 5090, 5155, 5265, 5330, 5395, 5440, 5505, 5570, 5699, 6370, 6545, 6580, 6595, 6610
Offset: 1

Views

Author

David Consiglio, Jr., May 12 2021

Keywords

Examples

			340 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4
    = 2^4 + 3^4 + 3^4 + 3^4 + 3^4
so 340 is a term of this sequence.

Links

Crossrefs

Cf. A003339, A309763, A342685, A343702, A344237, A344243, A345559.

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 >= 2])
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])

A344518 Numbers that are the sum of five positive fifth powers in four or more ways.

Original entry on oeis.org

287618651, 1386406515, 1763135232, 2494769760, 2619898293, 3096064443, 3291315732, 3749564512, 4045994624, 5142310350, 5183605813, 5658934676, 5880926107, 7205217018, 7401155424, 7691215599, 8429499101, 8926086432, 9006349824, 9051501568, 9203796832
Offset: 1

Views

Author

David Consiglio, Jr., May 21 2021

Keywords

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. A342685, A342686, A342687, A342688, A342687, A344519, A345718, A345863, 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, 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])

A344644 Numbers that are the sum of four fifth powers in two or more ways.

Original entry on oeis.org

51445, 876733, 1646240, 3558289, 4062500, 5687000, 7962869, 8227494, 9792364, 9924675, 10908544, 12501135, 15249850, 18317994, 18804544, 20611151, 20983875, 21297837, 23944908, 24201342, 24598407, 27806867, 28055456, 29480343, 31584102, 32557875, 32814683, 35469555, 40882844, 45177175
Offset: 1

Views

Author

David Consiglio, Jr., May 25 2021

Keywords

Examples

			1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5

Links

Crossrefs

Cf. A003349, A309763, A342685, A344645, A345010, A345337.

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, 4):
    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])

A345507 Numbers that are the sum of six fifth powers in two or more ways.

Original entry on oeis.org

4098, 4129, 4340, 5121, 7222, 11873, 20904, 36865, 51447, 51478, 51509, 51689, 51720, 51931, 52470, 52501, 52712, 53493, 54571, 54602, 54813, 55594, 57695, 59222, 59253, 59464, 60245, 62346, 63146, 66997, 67586, 68253, 68284, 68495, 68906, 68937, 69148, 69276
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			4129 is a term because 4129 = 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

Links

Crossrefs

Cf. A003351, A342685, A345559, A345604, A345605, A346357.

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 >= 2])
    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 1-9 of 9 results.

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

Content is available under The OEIS End-User License Agreement.