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 1-3 of 3 results.

A273508 Values of A272701 that are the sum of a positive square and a positive cube in more than one way.

Original entry on oeis.org

36998208, 449519625, 2367885312, 8016025680, 9563569561, 14753560033, 26971693632, 28769256000, 61358997609, 151544659968, 225128651328, 278450575201, 282429583137, 310289733000, 310289733000, 327699806625, 498700534033, 513025643520, 578097000000
Offset: 1

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Author

Altug Alkan, May 23 2016

Keywords

Comments

Taxi-cab numbers (A001235) that are the sum of two nonzero squares in more than one way and also the sum of a positive square and a positive cube in more than one way.
Subsequence of A273498.
A001235(293) = 6^3*A001235(16) = 6^3*171288 = 36998208 is the least number with this property.
14753560033 = 1453*2677*3793 is the first term that is in A272935.
Obviously, in this sequence there are perfect powers infinitely many times.

Examples

			36998208 is a term because 36998208 = 102^3 + 330^3 = 144^3 + 324^3 = 1728^2 + 324^3 = 5832^2 + 144^3 = 648^2 + 6048^2 = 1728^2 + 5832^2.

Crossrefs

Cf. A001235, A007692, A054402, A272701, A273498.

Extensions

a(2)-a(19) from Giovanni Resta, May 24 2016

A273354 Least number that is the sum of 2 positive cubes in exactly n ways and also the sum of 2 positive squares in exactly n ways.

Original entry on oeis.org

2, 4624776
Offset: 1

Views

Author

Altug Alkan, May 20 2016

Keywords

Comments

4624776 is the first term of A272701.
A011541(k) is not the sum of two nonzero squares for 2 <= k <= 6.
If it exists, what is the a(3)?

Examples

			a(1) = 2 because 2 = 1^3 + 1^3 = 1^2 + 1^2.
a(2) = 4624776 because 4624776 = 51^3 + 165^3 = 72^3 + 162^3 = 1026^2 + 1890^2 = 1350^2 + 1674^2.

Crossrefs

Cf. A001235, A011541, A016032, A272701.

A274367 Taxi-cab numbers (A001235) that are of the form x^2 + y^4 in more than one way (x, y > 0).

Original entry on oeis.org

27445392, 1644443281, 2367885312, 5687433577, 112416325632, 208265121792, 900069054976, 1976398601697, 6735639678976, 9698858237952, 9911785815477, 14585606569872, 15283760730112, 18156501172017, 23295727931392, 29871321586561, 33510832422912, 67250060669952
Offset: 1

Views

Author

Altug Alkan, Jun 19 2016

Keywords

Comments

A272701(3) = 27445392 is the least number with the property that sequence focuses on.
If n = a^3 + b^3 = c^3 + d^3 = x^2 + y^4 = z^2 + t^4, then n*k^12 = (a*k^4)^3 + (b*k^4)^3 = (c*k^4)^3 + (d*k^4)^3 = (x*k^6)^2 + (y*k^3)^4 = (z*k^6)^2 + (t*k^3)^4. So if n is this sequence, then n*k^12 is also in this sequence for all k > 1.

Examples

			27445392 is a term because 27445392 = 141^3 + 291^3 = 198^3 + 270^3 = 756^2 + 72^4 = 5076^2 + 36^4.
112416325632 is a term because 112416325632 = 27445392*2^12.

Crossrefs

Cf. A001235, A111925, A272701.

Extensions

a(2)-a(18) from Giovanni Resta, Jun 19 2016
Showing 1-3 of 3 results.

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