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.

A003349 Numbers that are the sum of 4 positive 5th powers.

Original entry on oeis.org

4, 35, 66, 97, 128, 246, 277, 308, 339, 488, 519, 550, 730, 761, 972, 1027, 1058, 1089, 1120, 1269, 1300, 1331, 1511, 1542, 1753, 2050, 2081, 2112, 2292, 2323, 2534, 3073, 3104, 3128, 3159, 3190, 3221, 3315, 3370, 3401, 3432, 3612, 3643, 3854, 4096, 4151, 4182, 4213
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Examples

			From _David A. Corneth_, Aug 03 2020: (Start)
670593 is in the sequence as 670593 = 1^5 + 8^5 + 10^5 + 14^5.
862512 is in the sequence as 862512 = 7^5 + 9^5 + 12^5 + 14^5.
1892695 is in the sequence as 1892695 = 1^5 + 1^5 + 5^5 + 18^5. (End)

Links

Crossrefs

Cf. A000584, A003338, A003348, A003350, A344642, A344644.

Programs

  • Mathematica
    f@n_:= Select[Range@n,IntegerPartitions[#,{4},Range@(n^(1/5))^5] != {} &]; f@10000 (* Hans Rudolf Widmer, Dec 04 2022 *)

Extensions

Incorrect program removed by David A. Corneth, Aug 03 2020

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])

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

A344645 Numbers that are the sum of four fifth powers in exactly two ways.

Original entry on oeis.org

51445, 876733, 1646240, 3558289, 4062500, 5687000, 7962869, 8227494, 9792364, 9924675, 10908544, 12501135, 15249850, 18317994, 18804544, 20611151, 20983875, 21297837, 23944908, 24201342, 24598407, 27806867, 28055456, 29480343, 31584102, 32557875, 32814683, 35469555, 40882844, 45177175
Offset: 1

Views

Author

David Consiglio, Jr., May 25 2021

Keywords

Comments

Differs from A344644 at term 508 because 1479604544 = 3^5 + 49^5 + 53^5 + 62^5 = 14^5 + 37^5 + 52^5 + 65^5 = 19^5 + 37^5 + 45^5 + 67^5

Examples

			1646240 is a term because 1646240 = 9^5 + 15^5 + 15^5 + 15^5 = 11^5 + 13^5 + 13^5 + 17^5

Links

Crossrefs

Cf. A342686, A344193, A344642, A344644.

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, 4):
    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])

A344641 Numbers that are the sum of three positive fifth powers in exactly one way.

Original entry on oeis.org

3, 34, 65, 96, 245, 276, 307, 487, 518, 729, 1026, 1057, 1088, 1268, 1299, 1510, 2049, 2080, 2291, 3072, 3127, 3158, 3189, 3369, 3400, 3611, 4150, 4181, 4392, 5173, 6251, 6282, 6493, 7274, 7778, 7809, 7840, 8020, 8051, 8262, 8801, 8832, 9043, 9375, 9824, 10902, 10933, 11144, 11925, 14026, 15553, 15584, 15795
Offset: 1

Views

Author

David Consiglio, Jr., May 25 2021

Keywords

Comments

Differs from A003348 at term 44785 because 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5. [Corrected by Patrick De Geest, Dec 27 2024]

Examples

			65 is a term because 65 = 1^5 + 2^5 + 2^5.

Links

Crossrefs

Cf. A003348, A344188, A344642.

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, 3):
    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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