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 1-6 of 6 results.

A345593 Numbers that are the sum of nine fourth powers in nine or more ways.

Original entry on oeis.org

8259, 9299, 9539, 10709, 10819, 10884, 10949, 10964, 11124, 11444, 11573, 11668, 11684, 11924, 12099, 12164, 12339, 12404, 12549, 12708, 12773, 12853, 12918, 12948, 13013, 13139, 13204, 13269, 13284, 13349, 13379, 13444, 13509, 13524, 13589, 13764, 13829
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			9299 is a term because 9299 = 1^4 + 1^4 + 1^4 + 2^4 + 6^4 + 6^4 + 6^4 + 6^4 + 8^4 = 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 8^4 + 8^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 7^4 + 9^4 = 1^4 + 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 6^4 + 6^4 + 9^4 = 2^4 + 2^4 + 2^4 + 2^4 + 3^4 + 4^4 + 7^4 + 7^4 + 8^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 6^4 + 6^4 + 7^4 + 8^4 = 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 7^4 = 2^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 + 6^4 + 7^4 + 7^4 = 3^4 + 3^4 + 4^4 + 4^4 + 4^4 + 4^4 + 4^4 + 6^4 + 9^4 = 3^4 + 3^4 + 4^4 + 6^4 + 6^4 + 6^4 + 6^4 + 6^4 + 7^4.

Links

Crossrefs

Cf. A345548, A345584, A345592, A345594, A345602, A345626, A345851.

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, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])

A345625 Numbers that are the sum of nine fifth powers in eight or more ways.

Original entry on oeis.org

1431398, 1431640, 1531397, 1952415, 1969221, 2247917, 2530399, 2596936, 2652563, 2652860, 2736790, 2851254, 2965588, 3088909, 3148674, 3273590, 3297416, 3329120, 3329362, 3332244, 3336895, 3345442, 3345653, 3353186, 3361614, 3362217, 3364738, 3378178, 3553641
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			1431640 is a term because 1431640 = 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 1^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 2^5 + 2^5 + 3^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5.

Links

Crossrefs

Cf. A345592, A345616, A345624, A345626, A345640, A346343.

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, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 8])
    for x in range(len(rets)):
        print(rets[x])

A346344 Numbers that are the sum of nine fifth powers in exactly nine ways.

Original entry on oeis.org

1969221, 2596936, 3353186, 3378178, 3923426, 3981447, 4094027, 4096729, 4112329, 4114188, 4129465, 4137209, 4147736, 4170112, 4172994, 4254304, 4303773, 4410482, 4475846, 4477936, 4483379, 4485480, 4501441, 4543232, 4652011, 4691855, 4724015, 4733970, 4750241
Offset: 1

Views

Author

David Consiglio, Jr., Jul 13 2021

Keywords

Comments

Differs from A345626 at term 14 because 4157156 = 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 9^5 + 21^5 = 1^5 + 1^5 + 3^5 + 4^5 + 5^5 + 5^5 + 8^5 + 8^5 + 21^5 = 1^5 + 4^5 + 4^5 + 8^5 + 10^5 + 12^5 + 12^5 + 16^5 + 19^5 = 1^5 + 4^5 + 4^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 19^5 = 5^5 + 5^5 + 5^5 + 5^5 + 7^5 + 9^5 + 15^5 + 17^5 + 18^5 = 3^5 + 3^5 + 5^5 + 6^5 + 9^5 + 10^5 + 16^5 + 16^5 + 18^5 = 1^5 + 1^5 + 5^5 + 5^5 + 13^5 + 13^5 + 15^5 + 15^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 10^5 + 14^5 + 16^5 + 16^5 + 17^5 = 11^5 + 11^5 + 12^5 + 12^5 + 12^5 + 12^5 + 13^5 + 16^5 + 17^5 = 2^5 + 2^5 + 2^5 + 5^5 + 12^5 + 15^5 + 16^5 + 16^5 + 16^5.

Examples

			1969221 is a term because 1969221 = 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 12^5 + 12^5 + 13^5 + 16^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 12^5 + 12^5 + 13^5 + 16^5 = 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 + 15^5 = 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 + 15^5 = 1^5 + 4^5 + 5^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 + 15^5 = 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 + 14^5 = 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 + 14^5.

Links

Crossrefs

Cf. A345626, A345851, A346334, A346343, A346345, A346354.

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, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 9])
    for x in range(len(rets)):
        print(rets[x])

A345617 Numbers that are the sum of eight fifth powers in nine or more ways.

Original entry on oeis.org

8742208, 15539667, 18913169, 19987308, 20135313, 21505583, 21512966, 21563089, 21727552, 22237510, 22256608, 22438990, 22545600, 22686818, 22932525, 23106589, 23122550, 23189782, 23221517, 23287858, 23346048, 23477344, 23798742, 23847285, 23931325, 24138358
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			15539667 is a term because 15539667 = 1^5 + 1^5 + 2^5 + 10^5 + 12^5 + 17^5 + 18^5 + 26^5 = 1^5 + 1^5 + 7^5 + 7^5 + 10^5 + 16^5 + 19^5 + 26^5 = 1^5 + 4^5 + 7^5 + 9^5 + 13^5 + 13^5 + 13^5 + 27^5 = 1^5 + 7^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 27^5 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 16^5 + 23^5 + 24^5 = 3^5 + 5^5 + 10^5 + 19^5 + 19^5 + 20^5 + 20^5 + 21^5 = 3^5 + 10^5 + 12^5 + 12^5 + 18^5 + 18^5 + 20^5 + 24^5 = 4^5 + 11^5 + 13^5 + 13^5 + 15^5 + 15^5 + 22^5 + 24^5 = 5^5 + 6^5 + 13^5 + 15^5 + 15^5 + 19^5 + 20^5 + 24^5 = 6^5 + 9^5 + 11^5 + 11^5 + 15^5 + 21^5 + 22^5 + 22^5.

Crossrefs

Cf. A345584, A345616, A345618, A345626, A345631, A346334.

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, 8):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])

A345627 Numbers that are the sum of nine fifth powers in ten or more ways.

Original entry on oeis.org

4157156, 4492410, 4510461, 4915538, 4948274, 5005474, 5015506, 5179747, 5219655, 5252477, 5739988, 5756794, 6323426, 6326519, 6382443, 6423394, 6654999, 6705284, 6793170, 6861218, 7101038, 7147645, 7147656, 7148679, 7266240, 7280391, 7283268, 7314187, 7413493
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			4492410 is a term because 4492410 = 1^5 + 1^5 + 2^5 + 3^5 + 5^5 + 7^5 + 7^5 + 13^5 + 21^5 = 1^5 + 2^5 + 6^5 + 10^5 + 11^5 + 11^5 + 14^5 + 16^5 + 19^5 = 1^5 + 6^5 + 7^5 + 8^5 + 9^5 + 9^5 + 14^5 + 18^5 + 18^5 = 2^5 + 5^5 + 6^5 + 6^5 + 7^5 + 15^5 + 15^5 + 16^5 + 18^5 = 2^5 + 5^5 + 6^5 + 10^5 + 10^5 + 11^5 + 11^5 + 15^5 + 20^5 = 3^5 + 3^5 + 7^5 + 7^5 + 9^5 + 12^5 + 13^5 + 18^5 + 18^5 = 3^5 + 3^5 + 8^5 + 8^5 + 8^5 + 12^5 + 12^5 + 17^5 + 19^5 = 3^5 + 4^5 + 6^5 + 7^5 + 8^5 + 13^5 + 14^5 + 16^5 + 19^5 = 4^5 + 4^5 + 4^5 + 7^5 + 11^5 + 11^5 + 13^5 + 18^5 + 18^5 = 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 16^5 + 17^5 + 18^5.

Links

Crossrefs

Cf. A345594, A345618, A345626, A345642, A346345.

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, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 10])
    for x in range(len(rets)):
        print(rets[x])

A345641 Numbers that are the sum of ten fifth powers in nine or more ways.

Original entry on oeis.org

1192180, 1226654, 1242437, 1431399, 1431430, 1431641, 1431672, 1431883, 1432453, 1432664, 1434765, 1439174, 1439416, 1441695, 1442718, 1447602, 1448447, 1455346, 1455377, 1464166, 1464377, 1464408, 1474431, 1474462, 1475485, 1491978, 1497619, 1505660, 1531398
Offset: 1

Views

Author

David Consiglio, Jr., Jun 20 2021

Keywords

Examples

			1226654 is a term because 1226654 = 1^5 + 1^5 + 4^5 + 5^5 + 7^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 = 1^5 + 1^5 + 5^5 + 7^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 = 1^5 + 2^5 + 2^5 + 4^5 + 6^5 + 10^5 + 12^5 + 12^5 + 12^5 + 13^5 = 1^5 + 2^5 + 2^5 + 4^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 = 1^5 + 3^5 + 3^5 + 3^5 + 7^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 7^5 + 8^5 + 12^5 + 13^5 + 14^5 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 5^5 + 10^5 + 13^5 + 13^5 + 13^5 = 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 8^5 + 9^5 + 16^5 = 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 8^5 + 9^5 + 16^5.

Links

Crossrefs

Cf. A345602, A345626, A345640, A345642, A346354.

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, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v >= 9])
    for x in range(len(rets)):
        print(rets[x])
Showing 1-6 of 6 results.

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

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