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 1-7 of 7 results.

A014439 Differences between two positive cubes in exactly 1 way.

Original entry on oeis.org

7, 19, 26, 37, 56, 61, 63, 91, 98, 117, 124, 127, 152, 169, 189, 208, 215, 217, 218, 271, 279, 296, 316, 331, 335, 342, 386, 387, 397, 448, 469, 485, 488, 504, 511, 513, 547, 602, 604, 631, 657, 665, 702, 784, 817, 819, 866, 875, 919, 936, 973, 988, 992
Offset: 1

Views

Author

Glen Burch (gburch(AT)erols.com)

Keywords

Links

Crossrefs

Cf. A000578, A038593, A181123, A034179 (more than one way), A014440 (exactly two ways), A265625 (more than two ways), A014441 (exactly three ways), A333376, A333377.

Programs

  • Maple
    N:= 1000: # to get all terms <= N
X:= floor(sqrt(N/3)):
V:= Vector(N):
for x from 2 to X do
  if x^3 > N then
     y0:= iroot(x^3-N, 3);
     if x^3 - y0^3 > N then y0:= y0+1 fi;
  else y0:= 1 fi;
  for y from y0 to x-1 do
     V[x^3 - y^3] := V[x^3 - y^3]+1
  od
od: select(t -> V[t] = 1, [$1..N]); # Robert Israel, Dec 11 2015
  • Mathematica
    r = 992; p = 3; Sort@Drop[Flatten@Select[Tally@Reap[Do[n = i^p - j^p; If[n <= r, Sow[n]], {i, Ceiling[(r/p)^(1/(p - 1))]}, {j, i}]][[2, 1]], #[[2]] == 1 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Corrected and extended by Don Reble, Nov 19 2006

A014440 Differences between two positive cubes in exactly 2 ways.

Original entry on oeis.org

721, 728, 999, 5768, 5824, 5859, 7992, 8911, 9919, 10621, 12663, 12824, 19467, 19656, 23877, 25669, 26973, 27937, 28063, 34209, 35208, 35929, 41743, 43561, 46144, 46592, 46872, 49959, 53144, 63936, 68857, 68913, 71288, 77779, 79352, 80379, 84968, 90125
Offset: 1

Views

Author

Glen Burch (gburch(AT)erols.com)

Keywords

Links

Crossrefs

Cf. A000578, A181123, A014439 (exactly one way), A034179 (more than one way), A265625 (more than two ways), A014441 (exactly three ways), A333376, A333377.

Programs

  • Mathematica
    r = 90125; p = 3; Sort@Drop[Flatten@Select[Tally@Reap[Do[n = i^p - j^p; If[n <= r, Sow[n]], {i, Ceiling[(r/p)^(1/(p - 1))]}, {j, i}]][[2, 1]], #[[2]] == 2 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Extended by Don Reble, Nov 19 2006

A014441 Differences between two positive cubes in exactly 3 ways.

Original entry on oeis.org

3367, 26936, 90909, 152551, 205352, 215488, 420875, 622232, 625177, 727272, 754299, 757701, 845208, 1147627, 1154881, 1220408, 1642816, 1723904, 2113921, 2454543, 2741256, 3056473, 3367000, 3442887, 3492125, 4481477, 4977856, 5001416, 5544504, 5818176
Offset: 1

Views

Author

Glen Burch (gburch(AT)erols.com)

Keywords

Links

Crossrefs

Cf. A000578, A181123, A014439 (exactly one way), A034179 (more than one way), A014440 (exactly two ways), A265625 (more than two ways), A333376 (exactly 4 ways), A333377 (exactly 5 ways).

Programs

  • Mathematica
    r = 5818176; p = 3; Sort@Drop[Flatten@Select[Tally@Reap[Do[n = i^p - j^p; If[n <= r, Sow[n]], {i, Ceiling[(r/p)^(1/(p - 1))]}, {j, i}]][[2, 1]], #[[2]] == 3 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Extended by Don Reble, Nov 19 2006

A333376 Differences between two positive cubes in exactly 4 ways.

Original entry on oeis.org

4118877, 32951016, 52324993, 94287375, 111209679, 214435711, 263608128, 418599944, 442245349, 514859625, 754299000, 889677432, 995635368, 1080305856, 1147627000, 1715485688, 2108865024, 2545759125, 3002661333, 3348799552, 3537962792, 3701994688, 4118877000, 4304670552
Offset: 1

Views

Author

Giovanni Resta, Mar 17 2020

Keywords

Examples

			4118877 = 162^3 - 51^3 = 165^3 - 72^3 = 178^3 - 115^3 = 678^3 - 675^3.

Links

Crossrefs

Cf. A014439, A014440, A014441, A181123, A034179, A265625, A333377, A098110.
Subsequence of A265625.

Formula

a(1) = A098110(4).

A333377 Differences between two positive cubes in exactly 5 ways.

Original entry on oeis.org

1412774811, 11302198488, 38144919897, 90417587904, 105443078832, 176596851375, 305159359176, 370544908608, 484581760173, 723340703232, 843544630656, 1029912837219, 1238805803151, 1412774811000, 1808088149952, 1880403273441, 2441274873408, 2846963128464, 2863636114248
Offset: 1

Views

Author

Giovanni Resta, Mar 17 2020

Keywords

Examples

			1412774811 = 1134^3 - 357^3 = 1155^3 - 504^3 = 1246^3 - 805^3 = 2115^3 - 2004^3 = 4746^3 - 4725^3.

Links

Crossrefs

Cf. A014439, A014440, A014441, A181123, A034179, A265625, A333376, A098110.

Formula

a(1) = A098110(5).

A034179 Difference between two positive cubes in more than one way.

Original entry on oeis.org

721, 728, 999, 3367, 5768, 5824, 5859, 7992, 8911, 9919, 10621, 12663, 12824, 19467, 19656, 23877, 25669, 26936, 26973, 27937, 28063, 34209, 35208, 35929, 41743, 43561, 46144, 46592, 46872, 49959, 53144, 63936, 68857, 68913, 71288, 77779
Offset: 1

Views

Author

Erich Friedman

Keywords

Links

Crossrefs

Cf. A014439, A014440, A014441, A333376, A333377, A181123, A265625.

Programs

  • Mathematica
    fQ[n_] := Block[{r = Reduce[0 < y < x && n == x^3 - y^3, {x, y}, Integers]}, If[r === False || Head[r] === And, False, Length[r] >= 2]]; Select[ Range[77780], If[ fQ[#], Print[#]; True, False] &] (* Jean-François Alcover, Apr 11 2011 *)
With[{nn=50},Take[Sort[Transpose[Select[Tally[#[[2]]-#[[1]]&/@Subsets[ Range[ nn*20]^3,{2}]],#[[2]]>1&]][[1]]],nn]] (* Harvey P. Dale, Mar 09 2016 *)

Extensions

Extended by Ray Chandler, Nov 29 2008
Offset corrected by Giovanni Resta, Mar 17 2020

A098110 Smallest number that is the difference between two positive cubes in n ways.

Original entry on oeis.org

7, 721, 3367, 4118877, 1412774811, 424910390480793
Offset: 1

Views

Author

Jeff Burch, Sep 23 2004

Keywords

Comments

a(7) <= 15490327057569000, a(8) <= 123922616460552000. - Giovanni Resta, Mar 19 2020

Examples

			Pairs (x, y) such that x^3 - y^3 = a(1), ..., a(6):
7 = (2, 1);
721 = (16, 15), (9, 2);
3367 = (34, 33), (16, 9), (15, 2)l
4118877 = (162, 51), (165, 72), (178, 115), (678, 675);
1412774811 = (1134, 357), (1155, 504), (1246, 805), (2115, 2004), (4746, 4725);
424910390480793 = (596001, 595602), (317982, 316575), (141705, 134268), (83482, 53935), (77385, 33768), (75978, 23919).

Crossrefs

Cf. A014439, A014440, A014441, A181123, A034179, A265625, A333376, A333377.
Cf. A011541,A047696.

Extensions

a(6) from Giovanni Resta, Mar 19 2020
Showing 1-7 of 7 results.

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