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.

A363957 Intersection of A035046 and A226777.

Original entry on oeis.org

1124864, 21952000, 82312875, 322828856, 916132832, 36859543552, 69731032896, 242620354053, 719323136000, 2697228288000, 6864416425125, 8712567840033, 10516413792429, 10578455953408, 16140568923648, 30019840638976, 35790185383875, 67052070434376, 72762401500992
Offset: 1

Views

Author

Jacob Natzke, Jun 29 2023

Keywords

Comments

This sequence is related to Beal's Conjecture (A^x + B^y = C^z), equal to C^z, A^5+B^3 = C^z.

Examples

			916132832 is equal to 62^5. 31^5 + 961^3 = 62^5.
		

Crossrefs

A051388 Numbers whose 4th power can be expressed as the sum of two positive cubes in more than one way.

Original entry on oeis.org

1729, 2457, 4104, 4914, 4977, 8001, 8216, 10773, 13832, 15561, 16263, 19656, 20683, 32832, 39312, 39816, 40033, 46683, 64008, 64232, 65728, 66339, 80236, 86184, 110656, 110808, 124336, 124488, 127062, 130104, 132678, 132867, 134379, 149389, 157248, 165464, 166887, 171288
Offset: 1

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Author

Keywords

Examples

			1729^4 = 1729^3 + 20748^3 = 15561^3 + 17290^3.
		

Crossrefs

Programs

  • PARI
    for(i=1, 10^5, x=i^4; c=0; for(j=1, floor(sqrtn(x/2,3)), if(ispower(x-j^3,3), c++)); if(c>1, print(i" "c))) \\ Donovan Johnson, Aug 03 2009

Extensions

More terms from John W. Layman, Feb 24 2003
a(18)-a(24) from Donovan Johnson, Aug 03 2009
a(25)-a(38) from Donovan Johnson, Dec 03 2010

A226950 Higher powers having partitions into distinct higher powers in more than one way.

Original entry on oeis.org

7449150177, 8936757492481, 11587386200625, 22449633661000, 30511719124992, 36443545848801, 283680450809856, 583096733580816, 613579106939841, 3958783819215057, 4098048384032001, 4556608567054336, 13469350037585841, 23887131799781376, 36604958689202176, 58634065908167841, 69952404620958561, 91953699475456000, 124976001535967232, 149272763796688896, 183001280170947121, 225430653627891712
Offset: 1

Views

Author

Keywords

Comments

A power m^k is called a higher power if k > 2, cf. A076467.

Examples

			a(1) = 7449150177 = 1953^3 = 1116^3 + 279^4 = 217^4 + 1736^3;
a(2) = 8936757492481 = 1729^4 = 1729^3 + 20748^3 = 15561^3 + 17290^3;
see link for more examples and more info.
		

Crossrefs

Cf. A051388, subsequence of A226777.

Programs

  • Haskell
    import qualified Data.Set as Set (split, filter)
    import Data.Set (Set, empty, size, insert, member)
    a226950 n = a226950_list !! (n-1)
    a226950_list = f a076467_list empty where
       f (x:xs) s | size s'' <= 1 = f xs (x `insert` s)
                  | otherwise     = x : f xs (x `insert` s)
                  where s'' = Set.filter ((`member` s) . (x -)) s'
                        (s', _) = Set.split (x `div` 2) s
Showing 1-3 of 3 results.