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.

A003351 Numbers that are the sum of 6 positive 5th powers.

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, 2052
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 03 2020: (Start)
90185 is in the sequence as 90185 = 2^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5.
104636 is in the sequence as 104636 = 1^5 + 3^5 + 3^5 + 4^5 + 5^5 + 10^5.
151173 is in the sequence as 151173 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 9^5. (End)

Links

Crossrefs

Cf. A000584, A003340, A003350, A003352, A345507, A346356.

A346357 Numbers that are the sum of six fifth powers in exactly two 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., Jul 13 2021

Keywords

Comments

Differs from A345507 at term 231 because 696467 = 1^5 + 6^5 + 8^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 13^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 13^5.

Examples

			4098 is a term 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.

Links

Crossrefs

Cf. A342686, A345507, A345814, A346279, A346356, 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, 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])

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])

A346278 Numbers that are the sum of seven fifth powers in exactly one way.

Original entry on oeis.org

7, 38, 69, 100, 131, 162, 193, 224, 249, 280, 311, 342, 373, 404, 435, 491, 522, 553, 584, 615, 646, 733, 764, 795, 826, 857, 975, 1006, 1030, 1037, 1061, 1068, 1092, 1123, 1154, 1185, 1216, 1217, 1248, 1272, 1279, 1303, 1334, 1365, 1396, 1427, 1459, 1490
Offset: 1

Views

Author

David Consiglio, Jr., Jul 13 2021

Keywords

Comments

Differs from A003352 at term 123 because 4099 = 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

Examples

			7 is a term because 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.

Links

Crossrefs

Cf. A003352, A345823, A346279, A346326, 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, 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])
Showing 1-5 of 5 results.

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

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