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.

A003339 Numbers that are the sum of 5 positive 4th powers.

Original entry on oeis.org

5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 260, 275, 290, 305, 320, 325, 340, 355, 370, 385, 405, 420, 435, 450, 500, 515, 530, 545, 560, 580, 595, 610, 625, 629, 644, 659, 674, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 04 2020: (Start)
22418 is in the sequence as 22418 = 1^4 + 2^4 + 7^4 + 10^4 + 10^4.
30004 is in the sequence as 30004 = 2^4 + 3^4 + 5^4 + 11^4 + 11^4.
39028 is in the sequence as 39028 = 5^4 + 5^4 + 7^4 + 11^4 + 12^4. (End)

Links

Crossrefs

Supersequence of A047716.
Cf. A000583, A003328, A003338, A003340, A003350, A344190, A344238.

Programs

  • Mathematica
    Select[Range[1000], AnyTrue[PowersRepresentations[#, 5, 4], First[#]>0&]&] (* Jean-François Alcover, Jul 18 2017 *)
  • Python
    from itertools import combinations_with_replacement as combs_with_rep
def aupto(limit):
  qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 4 <= limit]
  ss = set(sum(c) for c in combs_with_rep(qd, 5))
  return sorted(s for s in ss if s <= limit)
print(aupto(800)) # Michael S. Branicky, May 20 2021

A344189 Numbers that are the sum of four fourth powers in exactly one way.

Original entry on oeis.org

4, 19, 34, 49, 64, 84, 99, 114, 129, 164, 179, 194, 244, 274, 289, 304, 324, 339, 354, 369, 419, 434, 499, 514, 529, 544, 594, 609, 628, 643, 658, 673, 674, 708, 723, 738, 769, 784, 788, 803, 849, 868, 883, 898, 913, 963, 978, 1024, 1043, 1138, 1153, 1218, 1252, 1267, 1282, 1299, 1314, 1329, 1332, 1344, 1347, 1379, 1393
Offset: 1

Views

Author

David Consiglio, Jr., May 11 2021

Keywords

Comments

Differs from A003338 at term 14 because 259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4

Examples

			34 is a member of this sequence because 34 = 1^4 + 1^4 + 2^4 + 2^4

Links

Crossrefs

Cf. A003338, A025403, A344188, A344190, A344193, A344642.

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,4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k,v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

A344237 Numbers that are the sum of five fourth powers in exactly two 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, 4290, 4355, 4400, 4465, 4594, 4769, 4834, 5075, 5090, 5155, 5265, 5330, 5395, 5440, 5505, 5570, 5699, 6370, 6545, 6580, 6595, 6660, 6675
Offset: 1

Views

Author

David Consiglio, Jr., May 12 2021

Keywords

Comments

Differs from A344237 at term 31 because 4225 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4

Examples

			340 is a member of this sequence because 340 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4

Links

Crossrefs

Cf. A048927, A342686, A344190, A344193, A344238, A344244, A345814.

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])

A344643 Numbers that are the sum of five positive fifth powers in exactly one way.

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, 3136, 3160, 3191, 3222, 3253, 3316, 3347, 3371, 3402, 3433, 3464, 3558, 3613, 3644, 3675, 3855, 3886, 4128
Offset: 1

Views

Author

David Consiglio, Jr., May 25 2021

Keywords

Comments

Differs from A003350 at term 67 because 4097 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

Examples

			67 is a term because 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.

Links

Crossrefs

Cf. A003350, A342686, A344190, A344642, A346356.

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 == 1])
for x in range(len(rets)):
    print(rets[x])

Extensions

Name clarified by Patrick De Geest, Dec 24 2024

A345813 Numbers that are the sum of six fourth powers in exactly one ways.

Original entry on oeis.org

6, 21, 36, 51, 66, 81, 86, 96, 101, 116, 131, 146, 161, 166, 181, 196, 211, 226, 246, 306, 321, 326, 336, 371, 386, 401, 406, 436, 451, 466, 486, 501, 546, 561, 576, 581, 611, 626, 630, 641, 645, 660, 661, 675, 676, 690, 691, 705, 706, 710, 725, 740, 755, 756
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A003340 at term 20 because 261 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4.

Examples

			21 is a term because 21 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

Links

Crossrefs

Cf. A003340, A048929, A344190, A345814, A345823, A346356.

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 == 1])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-5 of 5 results.

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

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