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.

A022522 Nexus numbers (n+1)^6 - n^6.

Original entry on oeis.org

1, 63, 665, 3367, 11529, 31031, 70993, 144495, 269297, 468559, 771561, 1214423, 1840825, 2702727, 3861089, 5386591, 7360353, 9874655, 13033657, 16954119, 21766121, 27613783, 34655985, 43067087, 53037649, 64775151, 78504713, 94469815, 112933017, 134176679
Offset: 0

Views

Author

N. J. A. Sloane, Jun 14 1998

Keywords

References

  • J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.

Links

Crossrefs

Column k=5 of array A047969.
Beginning with n=1, a subsequence of A181125 (difference of two positive 6th powers). - Mathew Englander, Jun 01 2014
Cf. A008292, A022521, A022523.

Programs

Formula

G.f.: (1+x)*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^6. - Colin Barker, Dec 21 2012
a(n) = A005408(n) * A243201(n). - Mathew Englander, Jun 06 2014
a(n) = A001014(n+1) - A001014(n). - Wesley Ivan Hurt, Jun 06 2014
E.g.f.: (1 +62*x +270*x^2 +260*x^3 +75*x^4 +6*x^5)*exp(x). - G. C. Greubel, Aug 28 2019
G.f.: polylog(-6, x)*(1-x)/x. See the g.f. of Colin Barker (with expanded numerator), and the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021

Extensions

More terms from Colin Barker, Dec 21 2012

A181124 Difference of two positive 5th powers.

Original entry on oeis.org

0, 31, 211, 242, 781, 992, 1023, 2101, 2882, 3093, 3124, 4651, 6752, 7533, 7744, 7775, 9031, 13682, 15783, 15961, 16564, 16775, 16806, 24992, 26281, 29643, 31744, 32525, 32736, 32767, 40951, 42242, 51273, 55924, 58025, 58806, 59017, 59048, 61051
Offset: 1

Views

Author

T. D. Noe, Oct 06 2010

Keywords

Comments

Because x^5-y^5 = (x-y)(x^4+x^3*y+x^2*y^2+x*y^3+y^4), the difference of two 5th powers is a prime number only if x=y+1, in which case all the primes are in A121616. The number 7744 is the first of an infinite number of squares in this sequence.

Links

Crossrefs

Cf. A024352 (squares), A181123 (cubes), A147857 (4th powers), A181125-A181128 (6th to 9th powers)

Programs

  • Mathematica
    nn=10^9; p=5; Union[Reap[Do[n=i^p-j^p; If[n<=nn, Sow[n]], {i,Ceiling[(nn/p)^(1/(p-1))]}, {j,i}]][[2,1]]]

A303744 Numbers that are not a difference between same powers (greater than 1) of positive numbers.

Original entry on oeis.org

1, 2, 4, 6, 10, 14, 18, 22, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 222, 226, 230, 234, 238, 246, 250, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290
Offset: 1

Views

Author

Adam Kertesz, Apr 29 2018

Keywords

Comments

Apart from 1 and 4, all terms == 2 (mod 4). - Robert Israel, Jun 25 2018

Examples

			Odd numbers greater than 1 are differences of squares, so they are not here.
8 is not a term, 9 - 1: difference of two squares;
26 is not a term, 27 - 1: difference of two cubes.

Links

Crossrefs

Sequences of numbers that are difference of powers: A024352 (squares), A181123 (cubes).
And of further n-th powers: A147857 (4th), A181124 (5th), A181125 (6th), A181126 (7th), A181127 (8th), A181128 (9th).

Programs

  • Maple
    N:= 1000: # to get all terms <= N
S:= {1,2,4,seq(i,i=6..N,4)}:
for p from 3 to ilog2(N+1) do
  for n from 1 while n^p - (n-1)^p <= N do
    if n^p > N then m0:= ceil((n^p - N)^(1/p)) else m0:= 1 fi;
    for m from m0 to n-1 do
      v:= n^p-m^p;
      S:= S minus {v};
    od
od od:
sort(convert(S,list)); # Robert Israel, Jun 25 2018
Showing 1-3 of 3 results.

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

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