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 1-7 of 7 results.

A003341 Numbers that are the sum of 7 positive 4th powers.

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, 262, 277, 292, 307, 322, 327, 337, 342, 352, 357, 372, 387, 402, 407, 417, 422, 437, 452, 467, 482, 487, 502, 517, 532, 547, 562, 567, 577, 582, 592, 597, 612, 627
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 04 2020: (Start)
5971 is in the sequence as 5971 = 3^4 + 3^4 + 5^4 + 6^4 + 6^4 + 6^4 + 6^4.
12022 is in the sequence as 12022 = 1^4 + 2^4 + 7^4 + 7^4 + 7^4 + 7^4 + 7^4.
16902 is in the sequence as 16902 = 1^4 + 1^4 + 3^4 + 6^4 + 7^4 + 9^4 + 9^4. (End)

Links

Crossrefs

Cf. A000583, A003330, A003340, A003342, A003352, A047718, A345568, A345823.

Programs

  • Maple
    N:= 1000:
S1:= {seq(i^4,i=1..floor(N^(1/4)))}:
S2:= select(`<=`,{seq(seq(i+j,i=S1),j=S1)},N):
S4:= select(`<=`,{seq(seq(i+j,i=S2),j=S2)},N):
S6:= select(`<=`,{seq(seq(i+j,i=S2),j=S4)},N):
sort(convert(select(`<=`,{seq(seq(i+j,i=S1),j=S6)},N),list)); # Robert Israel, Jul 21 2019
  • Python
    from itertools import combinations_with_replacement as mc
def aupto(limit):
    qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 6 <= limit]
    ss = set(sum(c) for c in mc(qd, 7))
    return sorted(s for s in ss if s <= limit)
print(aupto(630)) # Michael S. Branicky, Jul 22 2021

A345559 Numbers that are the sum of six fourth powers in two or more 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, 2676, 2691, 2706, 2721, 2741, 2756, 2771, 2786, 2836, 2851, 2916, 2931, 2946, 2961, 3011, 3026, 3091, 3186, 3201, 3220, 3266
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

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. A003340, A344238, A345507, A345511, A345560, A345568, 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, 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])

A345569 Numbers that are the sum of seven fourth powers in three or more ways.

Original entry on oeis.org

2677, 2692, 2757, 2852, 2867, 2917, 2932, 2997, 3107, 3172, 3301, 3476, 3541, 3972, 4132, 4147, 4212, 4227, 4242, 4257, 4307, 4322, 4372, 4387, 4437, 4452, 4482, 4497, 4562, 4627, 4737, 4756, 4851, 4866, 4867, 4931, 4996, 5077, 5106, 5107, 5122, 5187, 5252
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			2692 is a term because 2692 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.

Links

Crossrefs

Cf. A345521, A345560, A345568, A345570, A345578, A345606, A345825.

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 >= 3])
    for x in range(len(rets)):
        print(rets[x])

A345577 Numbers that are the sum of eight fourth powers in two or more ways.

Original entry on oeis.org

263, 278, 293, 308, 323, 343, 358, 373, 388, 423, 438, 453, 503, 518, 533, 548, 563, 583, 598, 613, 628, 678, 693, 758, 773, 788, 803, 853, 868, 887, 902, 917, 932, 933, 967, 982, 997, 1028, 1043, 1047, 1062, 1108, 1127, 1142, 1157, 1172, 1222, 1237, 1283
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			278 is a term because 278 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A003342, A345532, A345568, A345578, A345586, A345610, A345834.

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, 8):
    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])

A345824 Numbers that are the sum of seven fourth powers in exactly two ways.

Original entry on oeis.org

262, 277, 292, 307, 342, 357, 372, 422, 437, 502, 517, 532, 547, 597, 612, 677, 772, 787, 852, 886, 901, 916, 966, 981, 1027, 1046, 1141, 1156, 1221, 1362, 1377, 1396, 1442, 1510, 1525, 1557, 1572, 1587, 1590, 1617, 1637, 1652, 1717, 1765, 1812, 1827, 1892
Offset: 1

Views

Author

David Consiglio, Jr., Jun 26 2021

Keywords

Comments

Differs from A345568 at term 61.

Examples

			277 is a term because 277 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

Links

Crossrefs

Cf. A345568, A345774, A345814, A345823, A345825, A345834, A346279.

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

A345520 Numbers that are the sum of seven cubes in two or more ways.

Original entry on oeis.org

131, 159, 166, 173, 185, 192, 211, 222, 229, 236, 243, 248, 255, 257, 262, 264, 269, 274, 276, 281, 283, 285, 288, 290, 292, 295, 299, 300, 302, 307, 309, 311, 314, 318, 320, 321, 325, 332, 333, 337, 339, 340, 344, 346, 348, 351, 353, 355, 358, 359, 360, 363
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			159 is a term because 159 = 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 4^3.

Links

Crossrefs

Cf. A003330, A345479, A345511, A345521, A345532, A345568, A345774.

Programs

  • Python
    from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**3 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 >= 2])
    for x in range(len(rets)):
        print(rets[x])

A345605 Numbers that are the sum of seven fifth powers in two or more ways.

Original entry on oeis.org

4099, 4130, 4161, 4341, 4372, 4583, 5122, 5153, 5364, 6145, 7223, 7254, 7465, 8246, 10347, 11874, 11905, 12116, 12897, 14998, 19649, 20905, 20936, 21147, 21928, 24029, 28680, 36866, 36897, 37108, 37711, 37889, 39990, 40138, 44641, 51393, 51448, 51479, 51510
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			4130 is a term because 4130 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.

Links

Crossrefs

Cf. A003352, A345507, A345568, A345606, A345610, A346279.

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 >= 2])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-7 of 7 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.