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.

A093330 Maximal values in A038598.

Original entry on oeis.org

7, 12, 19, 28, 53, 55, 56, 88, 99, 117, 129, 189, 190, 203, 241, 243, 352, 377, 380, 423, 576, 687, 798, 799, 918, 1036, 1170, 1441, 1566, 1799, 2150, 2259, 2393, 2528, 2576, 2825, 3149, 3374, 3582, 4508, 4804, 5166, 6455, 6805, 8448, 8776, 9296, 9675, 9784
Offset: 1

Views

Author

Jeff Burch, May 11 2004

Keywords

Crossrefs

Cf. A038598.

Extensions

Offset corrected and a(1)=7 inserted by Sean A. Irvine, Jan 23 2021

A038593 Differences between positive cubes in 1, 2 or 3 ways: union of A014439, A014440 and A014441.

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, 721, 728, 784, 817, 819, 866, 875, 919, 936, 973, 988
Offset: 1

Views

Author

Keywords

Crossrefs

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] <= 3 and V[t]>=1, [$1..N]); # Robert Israel, Dec 10 2015
  • Mathematica
    r = 988; 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]], 0 < #[[2]] < 4 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Corrected by Don Reble, Nov 19 2006

A038597 Numbers whose square is a difference between 2 positive cubes in at least one way.

Original entry on oeis.org

13, 28, 49, 104, 147, 181, 189, 224, 351, 361, 388, 392, 507, 549, 588, 676, 756, 832, 1029, 1176, 1323, 1369, 1425, 1448, 1512, 1625, 1792, 1862, 1911, 1922, 2299, 2355, 2521, 2808, 2883, 2888, 3104, 3136, 3185, 3216, 3500, 3721, 3969, 4056, 4103, 4332
Offset: 1

Views

Author

Keywords

Crossrefs

Programs

  • PARI
    is(n)=my(N=n^2); for(k=sqrtnint(N,3)+1,(sqrtint(12*N-3)+3)\6, if(ispower(N-k^3,3), return(1))); 0 \\ Charles R Greathouse IV, Oct 28 2013
    
  • PARI
    mm=820188; cb=vector(mm); for(i=1, mm, cb[i]=i^3); mb=1420608; v=vector(mb); mx=mb^2; for(i=1, mm-1, for(j=i+1, mm, d=cb[j]-cb[i]; if(d<=mx, if(issquare(d, &r), v[r]=1), next(2)))); c=0; for(n=1, mb, if(v[n]==1, c++; write("b038597.txt", c " " n))) \\ Donovan Johnson, Oct 31 2013

Formula

a(n) = sqrt(A038596(n)). - M. F. Hasler, Oct 05 2013

Extensions

More terms from Jud McCranie

A038596 Squares that are a difference between 2 positive cubes.

Original entry on oeis.org

169, 784, 2401, 10816, 21609, 32761, 35721, 50176, 123201, 130321, 150544, 153664, 257049, 301401, 345744, 456976, 571536, 692224, 1058841, 1382976, 1750329, 1874161, 2030625, 2096704, 2286144, 2640625, 3211264, 3467044, 3651921, 3694084, 5285401, 5546025
Offset: 1

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Author

Keywords

Crossrefs

Programs

  • PARI
    is(n)=for(k=sqrtnint(n,3)+1,(sqrtint(12*n-3)+3)\6,if(ispower(n-k^3,3), return(issquare(n)))); 0 \\ Charles R Greathouse IV, Oct 28 2013
    
  • PARI
    mm=820188; cb=vector(mm); for(i=1, mm, cb[i]=i^3); mb=1420608; v=vector(mb); mx=mb^2; for(i=1, mm-1, for(j=i+1, mm, d=cb[j]-cb[i]; if(d<=mx, if(issquare(d, &r), v[r]=1), next(2)))); c=0; for(n=1, mb, if(v[n]==1, c++; write("b038596.txt", c " " n^2))) \\ Donovan Johnson, Oct 31 2013

Formula

a(n) = A038597(n)^2. - M. F. Hasler, Oct 05 2013

Extensions

More terms from Jud McCranie

A228946 Numbers m such that m^3 - k^3 is a square for some k < m, k > 0.

Original entry on oeis.org

8, 10, 14, 28, 32, 33, 40, 56, 57, 65, 71, 72, 74, 78, 90, 105, 112, 114, 126, 128, 130, 132, 140, 148, 154, 155, 160, 176, 193, 200, 217, 218, 224, 228, 250, 252, 260, 266, 273, 280, 284, 288, 296, 297, 305, 312, 329, 336, 344, 349, 350, 360, 392
Offset: 1

Views

Author

M. F. Hasler, Oct 05 2013

Keywords

Comments

See A038596 = A038597^2 for the possible values of n^3-k^3.

Crossrefs

Programs

Formula

a(n) = A066648(n)^(1/3). - Amiram Eldar, Mar 20 2025

A038594 Numbers n such that n and n+1 are differences between 2 positive cubes in at least one way.

Original entry on oeis.org

217, 386, 2168, 2169, 2401, 2716, 3087, 3752, 6516, 7351, 9423, 9576, 10107, 12096, 13084, 13480, 14769, 14832, 18486, 20312, 29763, 32464, 32760, 36631, 37296, 37448, 39815, 50310, 54405, 58329, 58807, 63656, 67544, 78344, 81711, 83285
Offset: 1

Views

Author

Keywords

Crossrefs

Formula

a(n) = A038595(n)-1. - M. F. Hasler, Oct 05 2013

A038595 Numbers n such that n and n-1 are differences between 2 positive cubes in at least one way.

Original entry on oeis.org

218, 387, 2169, 2170, 2402, 2717, 3088, 3753, 6517, 7352, 9424, 9577, 10108, 12097, 13085, 13481, 14770, 14833, 18487, 20313, 29764, 32465, 32761, 36632, 37297, 37449, 39816, 50311, 54406, 58330, 58808, 63657, 67545, 78345, 81712, 83286
Offset: 1

Views

Author

Keywords

Crossrefs

Formula

a(n) = A038594(n)+1. - M. F. Hasler, Oct 05 2013
Showing 1-7 of 7 results.