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 1-4 of 4 results.

A147857 Differences of two positive 4th powers.

Original entry on oeis.org

0, 15, 65, 80, 175, 240, 255, 369, 544, 609, 624, 671, 1040, 1105, 1215, 1280, 1295, 1695, 1776, 2145, 2320, 2385, 2400, 2465, 2800, 3439, 3471, 3840, 4015, 4080, 4095, 4160, 4641, 5265, 5904, 5936, 6095, 6305, 6480, 6545, 6560, 7599, 7825, 8080, 8704
Offset: 1

Views

Author

Max Alekseyev, Nov 15 2008, Nov 19 2008

Keywords

Comments

If n belongs to this sequence then so does n*m^4 for any positive integer m. Primitive elements (i.e., not of the form n*m^4 for m>1) are listed in A147858.
There is no square in this sequence except 0. - Altug Alkan, Apr 08 2016

Links

Crossrefs

Subsequence of A152044.
Cf. A147854, A147856, A147858

Programs

  • Maple
    N:= 10^4: # to get all terms <= N
Res:= {0}:
for a from 1 to floor(sqrt(N-2)) do
  if a^4 > N then bmin:= ceil((a^4-N)^(1/4)) else bmin:= 1 fi;
  Res:= Res union {seq(a^4-b^4, b=bmin..a-1)}
od:
sort(convert(Res,list)); # Robert Israel, Sep 28 2018
  • Mathematica
    nn = 50; Take[Union @@ Map[Differences, Union@ Map[Sort@ # &, Tuples[Range[Ceiling[nn/3]], {2}]]^4], nn] (* Michael De Vlieger, Apr 09 2016 *)

Extensions

Offset changed by Robert Israel, Sep 28 2018

A152043 Numbers expressible as the difference of two nonnegative cubes.

Original entry on oeis.org

0, 1, 7, 8, 19, 26, 27, 37, 56, 61, 63, 64, 91, 98, 117, 124, 125, 127, 152, 169, 189, 208, 215, 216, 217, 218, 271, 279, 296, 316, 331, 335, 342, 343, 386, 387, 397, 448, 469, 485, 488, 504, 511, 512, 513, 547, 602, 604, 631, 657, 665, 702, 721, 728, 729, 784
Offset: 1

Views

Author

Mark Taggart (mt2612f(AT)aol.com), Nov 21 2008

Keywords

Comments

Subsequence of A045980. - R. J. Mathar, Nov 28 2008
Contains A000578 as a subsequence. - Chandler

Examples

			E.g. 7=2^3-1^3, 8=2^3-0^3, 296=8^3-6^3.

Links

Crossrefs

Cf. A042965, A152044, A152045.
The Index to the OEIS lists many related sequences under "difference of two cubes". - N. J. A. Sloane, Dec 04 2008

Programs

  • PARI
    T=thueinit('z^3+1);
is(n)=n==0 || #select(v->v[1]<=0&&v[2]>=0, thue(T, n))>0 \\ Charles R Greathouse IV, Nov 29 2014

Extensions

Extended by Ray Chandler, Dec 04 2008

A152045 Numbers expressible as the difference of two nonnegative fifth powers.

Original entry on oeis.org

0, 1, 31, 32, 211, 242, 243, 781, 992, 1023, 1024, 2101, 2882, 3093, 3124, 3125, 4651, 6752, 7533, 7744, 7775, 7776, 9031, 13682, 15783, 15961, 16564, 16775, 16806, 16807, 24992, 26281, 29643, 31744, 32525, 32736, 32767, 32768, 40951, 42242
Offset: 1

Views

Author

Mark Taggart (mt2612f(AT)aol.com), Nov 21 2008

Keywords

Examples

			E.g. 31=2^5-1^5, 992=4^5-2^5.

Crossrefs

Contains A000584 as a subsequence. - Ray Chandler, Dec 04 2008
Cf. A042965, A152043, A152044.

Extensions

Extended by Ray Chandler, Dec 04 2008
Definition corrected by Harvey P. Dale, Jan 19 2018

A228760 Least positive integer x such that x and n*x are both differences of fourth powers.

Original entry on oeis.org

1, 179727600, 80, 1040, 16, 2320, 4080, 236187120, 76960, 240, 17680, 76960, 80, 1040, 1, 1, 15, 65520, 4851120, 224991600, 100880, 1728480, 27120, 1389920, 19578624, 1048560, 240, 2986560, 80, 80, 2465, 11232975, 65, 16, 80, 2320, 12240, 707200, 16, 6560
Offset: 1

Views

Author

Robert Israel, Sep 02 2013

Keywords

Comments

It's not obvious that a(n) exists for all n.
a(967) > 8*10^15 (if it exists). - Donovan Johnson, Sep 04 2013

Examples

			For n = 3, 80 = 3^4 - 1^4 and 3*80 = 4^4 - 2^4.

References

  • A. Choudhry, Indian J. pure appl. Math. 26(11) (1995), 1057-1061

Links

Crossrefs

Cf. A152044.

Programs

  • Maple
    T:= 10^12; N:= 100;  # to get solutions with n*a(n)<=T and n <= N
cmax := floor(fsolve('c'^4 - ('c'-1)^4 = T));
S:= {seq(seq(c^4 - a^4, a = ceil((max(0,c^4 - T))^(1/4))..c-1),c=1..cmax)}:
for n from 1 to N do
  B:= S intersect map(`*`,S,n);
  if B <> {} then
    A[n]:= min(B)/n;
    printf("a[%d] = %d\n",n,A[n]);
  end if
end do:  # Robert Israel, Sep 02 2013
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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