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 1-10 of 15 results. Next

A046093 Erroneous version of A230563.

Original entry on oeis.org

5, 9, 251, 2673, 1375298099, 106426514
Offset: 1

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Keywords

Comments

Both a(2) and a(6) are wrong.

A342904 Erroneous version of A230563.

Original entry on oeis.org

5, 27, 251, 2673, 1375298099, 106426514
Offset: 1

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Keywords

Comments

Included in accordance with OEIS policy of listing published but incorrect sequences to serve as pointers to the correct versions.

A342893 Smallest number that is the sum of three positive n-th powers in three ways.

Original entry on oeis.org

54, 5104, 811538
Offset: 2

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Author

N. J. A. Sloane, Apr 03 2021

Keywords

Examples

			a(2) = 54 = 1+4+49 = 4+25+25 = 9+9+36.
		

Crossrefs

A342903 a(n) is the smallest number that is the sum of n positive squares in two ways.

Original entry on oeis.org

50, 27, 28, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86
Offset: 2

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Author

N. J. A. Sloane, Apr 03 2021

Keywords

Comments

This is r(n,2,2) in Alter's notation.

Examples

			a(2) = 50 = 1+49 = 25+25.
a(3) = 27 = 1+1+25 = 9+9+9.
a(5) = 20 = 1+1+1+1+16 = 4+4+4+4+4.
		

Crossrefs

Formula

a(n) = n+15 for n >= 5.

A342902 a(n) is the smallest number that is the sum of n positive cubes in two ways.

Original entry on oeis.org

1729, 251, 219, 157, 158, 131, 132, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126
Offset: 2

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Author

N. J. A. Sloane, Apr 03 2021

Keywords

Comments

This is r(n,3,2) in Alter's notation.

Examples

			a(2) = 1729 = 12^3 + 1^3 = 10^3 + 9^3 (the famous Hardy-Ramanujan number).
a(3) = 251 = 5^3 + 5^3 + 1^3 = 6^3 + 3^3 + 2^3.
		

Crossrefs

Formula

a(n) = n+63 for n >= 9.

A343078 a(n) is the smallest number that is the sum of n positive 5th powers in two ways.

Original entry on oeis.org

1375298099, 51445, 4097, 4098, 4099, 4100, 4101, 4102, 4103, 4104, 4105, 4106, 4107, 4108, 4109, 4110, 4111, 4112, 4113, 4114, 4115, 4116, 4117, 4118, 4119, 4120, 4121, 4122, 4123, 4124, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067
Offset: 3

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Author

Sean A. Irvine, Apr 04 2021

Keywords

Comments

This is r(n,5,2) in Alter's notation.

Examples

			a(3) = 1375298099 = 3^5 + 54^5 + 62^5 = 24^5 + 28^5 + 67^5.
a(4) = 51445 = 4^5 + 7^5 + 7^5 + 7^5 = 5^5 + 6^5 + 6^5 + 8^5.
		

Crossrefs

Formula

a(n) = n + 1023 for n >= 33.

A343079 a(n) is the smallest number that is the sum of n positive 6th powers in two ways.

Original entry on oeis.org

160426514, 1063010, 1063011, 570947, 570948, 63232, 63233, 52489, 52490, 52491, 16393, 16394, 16395, 16396, 16397, 13122, 13123, 13124, 13125, 13126, 13127, 13128, 13129, 13130, 13131, 13132, 13133, 13134, 13135, 13136, 13137, 13138, 8225, 8226, 8227, 8228, 8229, 6592, 6593, 6594, 6595, 6596, 6597, 6598, 6599, 6600, 6601, 6602, 6603, 6604, 6605, 6606, 6607, 6608, 6609, 6610, 6611, 6612, 6613, 6614, 6615, 6616, 4160
Offset: 3

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Author

Sean A. Irvine, Apr 04 2021

Keywords

Comments

This is r(n,6,2) in Alter's notation.
Alter paper has a typographical error a(3)=106426514.

Examples

			a(3) = 160426514 = 3^6 + 19^6 + 22^6 = 10^6 + 15^6 + 23^6.
a(4) = 1063010 = 2^6 + 2^6 + 9^6 + 9^6 = 3^6 + 5^6 + 6^6 + 10^6.
		

Crossrefs

Formula

a(n) = n + 4095 for n >= 65.

A342895 Smallest number that is the sum of five positive n-th powers in three ways.

Original entry on oeis.org

29, 766, 4225, 13124675, 224688658
Offset: 2

Views

Author

N. J. A. Sloane, Apr 04 2021

Keywords

Comments

a(7) > 2*10^11. - Jon E. Schoenfield, Apr 11 2021

Examples

			From _Jon E. Schoenfield_, Apr 11 2021: (Start)
a(2) = 29 = 1^2 + 1^2 + 1^2 + 1^2 + 5^2
          = 1^2 + 1^2 + 3^2 + 3^2 + 3^2
          = 1^2 + 2^2 + 2^2 + 2^2 + 4^2.
.
a(3) = 766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3
           = 1^3 + 4^3 + 4^3 + 5^3 + 8^3
           = 2^3 + 2^3 + 4^3 + 7^3 + 7^3.
.
a(4) = 4225 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4
            = 2^4 + 4^4 + 4^4 + 6^4 + 7^4
            = 3^4 + 4^4 + 6^4 + 6^4 + 6^4.
.
a(5) = 13124675 =  1^5 +  9^5 + 10^5 + 20^5 + 25^5
                =  2^5 +  5^5 + 12^5 + 23^5 + 23^5
                = 16^5 + 19^5 + 20^5 + 20^5 + 20^5.
.
a(6) = 224688658 = 3^6 +  8^6 + 19^6 + 20^6 + 22^6
                 = 5^6 +  5^6 + 16^6 + 16^6 + 24^6
                 = 8^6 + 10^6 + 15^6 + 20^6 + 23^6. (End)
		

Crossrefs

Extensions

a(6) from Jinyuan Wang, Apr 11 2021

A342894 Smallest number that is the sum of four positive n-th powers in three ways.

Original entry on oeis.org

28, 1225, 16578, 1479604544, 1885800643779
Offset: 2

Views

Author

N. J. A. Sloane, Apr 04 2021

Keywords

Examples

			a(2) = 28 = 1+1+1+25 = 4+4+4+16 = 1+9+9+9.
		

Crossrefs

Extensions

a(5)-a(6) from Jinyuan Wang, Apr 10 2021

A342896 Smallest number that is the sum of six positive n-th powers in three ways.

Original entry on oeis.org

30, 221, 2676, 696467, 17886882
Offset: 2

Views

Author

N. J. A. Sloane, Apr 04 2021

Keywords

Examples

			From _Ilya Gutkovskiy_, Aug 12 2024: (Start)
a(6) = 17886882 = 1^6 + 8^6 + 8^6 + 12^6 + 12^6 + 15^6
                = 2^6 + 2^6 + 6^6 +  9^6 +  9^6 + 16^6
                = 3^6 + 5^6 + 6^6 +  6^6 + 10^6 + 16^6. (End)
		

Crossrefs

Extensions

a(6) from Jinyuan Wang, Apr 11 2021
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