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.

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A091414 Least number that is the sum of n positive n-th powers in at least 2 ways.

Original entry on oeis.org

50, 251, 259, 4097, 570947, 73310705, 647282661, 79327628290, 1077347903894, 1761813250036143, 2343908545594901
Offset: 2

Views

Author

Gabriel Cunningham (gcasey(AT)mit.edu), Mar 02 2004

Keywords

Comments

From Donovan Johnson, Sep 14 2008: (Start)
a(11) = 2^11 + 2^11 + 2^11 + 2^11 + 8^11 + 10^11 + 10^11 + 15^11 + 22^11 + 22^11 + 22^11 = 3^11 + 5^11 + 5^11 + 5^11 + 6^11 + 9^11 + 11^11 + 12^11 + 17^11 + 20^11 + 24^11.
a(12) = 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 2^12 + 9^12 + 9^12 + 9^12 + 15^12 + 19^12 = 3^12 + 5^12 + 5^12 + 10^12 + 10^12 + 10^12 + 10^12 + 12^12 + 12^12 + 17^12 + 17^12 + 18^12.
a(13) > 876*10^15. a(14) > 799*10^15. a(15) > 115*10^16. (End)

Examples

			a(3) = 251 because 251 = 1^3 + 5^3 + 5^3 = 2^3 + 3^3 + 6^3 and it is the smallest number that can be represented two ways as the sum of three third powers.

Crossrefs

a(2) = A048610(2), a(3) = A008917(1), a(4) = A185673(2). - Jonathan Sondow, Oct 24 2013
Cf. A230561, A230477.

Formula

a(n) <= A230477(n) for n > 1, with equality at least for n = 2 and inequality at least for n = 3, 4, 5. - Jonathan Sondow, Oct 24 2013

Extensions

More terms from David Wasserman, Mar 09 2006
a(11)-a(12) from Donovan Johnson, Sep 14 2008
Definition shortened by Jonathan Sondow, Oct 24 2013

A219329 Numbers that can be expressed as the sum of three nonnegative cubes in three ways.

Original entry on oeis.org

5104, 5832, 9288, 9729, 10261, 10773, 12104, 12221, 12384, 14175, 17604, 17928, 19034, 20691, 21412, 21888, 24416, 24480, 28792, 29457, 30528, 31221, 32850, 34497, 35216, 36288, 38259, 39339, 39376, 39528, 40060, 40097, 40832, 40851, 41033, 41040, 41364
Offset: 1

Views

Author

Kevin L. Schwartz and Christian N. K. Anderson, Apr 11 2013

Keywords

Comments

Index of A051343 = 9, superset of index of A025456 = 3.
Subset of A001239.

Examples

			a(1) = 5104 = 1^3+12^3+15^3 = 2^3+10^3+16^3 = 9^3+10^3+15^3.

Links

Crossrefs

Other sums of cubes: A025402, A025398, A024974, A001239, A008917.
Cf. A025456, A051343.
Cf. A025396.

Programs

  • Mathematica
    Select[Range[42000],Length[PowersRepresentations[#,3,3]]==3&] (* Harvey P. Dale, Sep 28 2016 *)

A384553 Primes p for which there exists more than one triple of primes q, r, s such that p^3 = q^3 + r^3 + s^3.

Original entry on oeis.org

28477, 33199, 49069, 234181, 300239, 403549, 463501, 958933, 982337, 1044227, 1352873, 1385861, 1713121, 1834321, 1994911, 2364673, 2531687, 2839927, 3048691, 3364553, 3546031, 3640543, 3897739, 3941711, 4000907, 4264219, 4273459, 4594399, 4599709, 4620037, 4924979
Offset: 1

Views

Author

Zhining Yang, Jun 03 2025

Keywords

Examples

			28477^3 = 3739^3 + 17203^3 + 26183^3 = 10781^3 + 11071^3 + 27361^3.
33199^3 = 2833^3 + 19081^3 + 30941^3 = 15187^3 + 24197^3 + 26647^3.
49069^3 =  661^3 + 37441^3 + 40343^3 = 22307^3 + 37243^3 + 38119^3.

Links

Crossrefs

Cf. A008917, A114923.
Previous Showing 11-13 of 13 results.

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

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