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.

A003340 Numbers that are the sum of 6 positive 4th powers.

Original entry on oeis.org

6, 21, 36, 51, 66, 81, 86, 96, 101, 116, 131, 146, 161, 166, 181, 196, 211, 226, 246, 261, 276, 291, 306, 321, 326, 336, 341, 356, 371, 386, 401, 406, 421, 436, 451, 466, 486, 501, 516, 531, 546, 561, 576, 581, 596, 611, 626, 630, 641, 645, 660, 661, 675, 676, 690
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 04 2020: (Start)
13090 is in the sequence as 13090 = 4^4 + 4^4 + 5^4 + 6^4 + 8^4 + 9^4.
17539 is in the sequence as 17539 = 2^4 + 3^4 + 4^4 + 5^4 + 9^4 + 10^4.
23732 is in the sequence as 23732 = 3^4 + 5^4 + 5^4 + 7^4 + 10^4 + 10^4. (End)

Links

Crossrefs

Cf. A000583, A003329, A003339, A003341, A003351, A345559, A345813.

Programs

  • Mathematica
    Select[Range[1000], AnyTrue[PowersRepresentations[#, 6, 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 + 5 <= limit]
    ss = set(sum(c) for c in combs_with_rep(qd, 6))
    return sorted(s for s in ss if s <= limit)
print(aupto(700)) # Michael S. Branicky, Jun 21 2021

A345814 Numbers that are the sum of six fourth powers in exactly two ways.

Original entry on oeis.org

261, 276, 291, 341, 356, 421, 516, 531, 596, 771, 885, 900, 965, 1140, 1361, 1509, 1556, 1571, 1636, 1811, 2180, 2596, 2611, 2661, 2691, 2706, 2721, 2741, 2756, 2771, 2786, 2836, 2931, 2946, 2961, 3011, 3026, 3091, 3186, 3201, 3220, 3266, 3285, 3300, 3315
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345559 at term 25 because 2676 = 1^4 + 1^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.

Examples

			276 is a term because 276 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A048930, A344237, A345559, A345813, A345815, A345824, A346357.

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

A345823 Numbers that are the sum of seven fourth powers in exactly one ways.

Original entry on oeis.org

7, 22, 37, 52, 67, 82, 87, 97, 102, 112, 117, 132, 147, 162, 167, 177, 182, 197, 212, 227, 242, 247, 322, 327, 337, 352, 387, 402, 407, 417, 452, 467, 482, 487, 562, 567, 577, 582, 592, 627, 631, 642, 646, 657, 661, 662, 676, 691, 692, 706, 707, 711, 721, 722
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A003341 at term 23 because 262 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.

Examples

			22 is a term because 22 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

Links

Crossrefs

Cf. A003341, A345773, A345813, A345824, A345833, A346278.

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

A344190 Numbers that are the sum of five fourth powers in exactly one way.

Original entry on oeis.org

5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 290, 305, 320, 325, 355, 370, 385, 405, 420, 435, 450, 500, 530, 545, 560, 580, 595, 610, 625, 629, 644, 659, 674, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800, 804, 819, 850, 865, 869, 899, 914, 929, 930, 949, 964, 979, 994, 1025, 1040
Offset: 1

Views

Author

David Consiglio, Jr., May 11 2021

Keywords

Comments

Differs from A003339 at term 17 because 260 = 1^4 + 1^4 + 1^4 + 1^4 + 4^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4

Examples

			35 is a member of this sequence because 35 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4

Links

Crossrefs

Cf. A003339, A048926, A344189, A344237, A344643, A345813.

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

A346356 Numbers that are the sum of six fifth powers in exactly one way.

Original entry on oeis.org

6, 37, 68, 99, 130, 161, 192, 248, 279, 310, 341, 372, 403, 490, 521, 552, 583, 614, 732, 763, 794, 825, 974, 1005, 1029, 1036, 1060, 1091, 1122, 1153, 1184, 1216, 1247, 1271, 1302, 1333, 1364, 1395, 1458, 1513, 1544, 1575, 1606, 1755, 1786, 1817, 1997, 2028
Offset: 1

Views

Author

David Consiglio, Jr., Jul 13 2021

Keywords

Comments

Differs from A003351 at term 93 because 4098 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

Examples

			6 is a term because 6 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.

Links

Crossrefs

Cf. A003351, A344643, A345813, A346278, 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 == 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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