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.

A022538 Nexus numbers (n+1)^22 - n^22.

Original entry on oeis.org

1, 4194303, 31376865305, 17560804984807, 2366593604971209, 129237518051251511, 3778199344740720913, 69877155246255218415, 910983925888773026417, 9015229097816388767119, 71402749386839761113321, 470658689525596656480023, 2659777439042418687564025
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Column k=21 of A047969.
Cf. A010810.

Programs

  • Magma
    [(n+1)^22 - n^22: n in [0..20]]; // G. C. Greubel, Feb 27 2018
  • Maple
    b:=22: a:=n->(n+1)^b-n^b: seq(a(n),n=0..18); # Muniru A Asiru, Feb 28 2018
  • Mathematica
    Table[(n+1)^22 - n^22, {n,0,20}] (* G. C. Greubel, Feb 27 2018 *)
  • PARI
    for(n=0,20, print1((n+1)^22 - n^22, ", ")) \\ G. C. Greubel, Feb 27 2018

Formula

a(n) = A010810(n+1) - A010810(n). - Michel Marcus, Feb 27 2018

Extensions

Terms a(12) onward added by G. C. Greubel, Feb 27 2018

A036100 Centered cube numbers: (n+1)^22 + n^22.

Original entry on oeis.org

1, 4194305, 31385253913, 17623567104025, 2401777977060041, 134005889633282761, 4041442752425255185, 77696797343421194513, 1058557878478449439345, 10984770902183611232881
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Can never be prime, as a(n) = (2n^2 + 2n + 1) * (n^20 + 10n^19 + 105n^18 + 660n^17 + 2945n^16 + 9892n^15 + 25942n^14 + 54384n^13 + 92530n^12 + 128988n^11 + 148070n^10 + 140152n^9 + 109136n^8 + 69498n^7 + 35819n^6 + 14704n^5 + 4693n^4 + 1122n^3 + 189n^2 + 20n + 1). a(2) is semiprime (see A001358). [Jonathan Vos Post, Aug 17 2011]

References

  • B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

Links

Crossrefs

Cf. A010810, A036098, A036099.

Programs

  • Magma
    [(n+1)^22+n^22: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
  • Mathematica
    Total/@(Partition[Range[0,10],2,1]^22) (* Harvey P. Dale, Jun 28 2015 *)

A013905 22^(5n+4).

Original entry on oeis.org

234256, 1207269217792, 6221821273427820544, 32064977213018365645815808, 165251092644282265779977014214656, 851643319086537701956194499721106030592, 4389056261830591470007906571986683114651910144, 22619580800770514778759787562400873673529752979243008
Offset: 0

Views

Author

N. J. A. Sloane, Dec 11 1996

Keywords

Links

Programs

Formula

a(n) = 5153632*a(n-1), a(0)=234256. - Vincenzo Librandi, May 28 2011
a(n) = 22^A016897(n) = A010810(5n+4) = A010810(A016897(n)). - Wesley Ivan Hurt, May 08 2014

A016907 (5n+4)^11.

Original entry on oeis.org

4194304, 31381059609, 4049565169664, 116490258898219, 1521681143169024, 12200509765705829, 70188843638032384, 317475837322472439, 1196683881290399744, 3909821048582988049, 11384956040305711104
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

If 5n+4 is a perfect square, that is for n=0,1,9,12,28,33,57,64,..., a(n)=A010810(j), where the indices j are listed in A047221. - R. J. Mathar, Apr 22 2008.

Links

Programs

Formula

G.f.: (x^11 +362797044*x^10 +280958106005*x^9 +14192390602560*x^8 +157922022917730*x^7 +565509776420088*x^6 +753319100251602*x^5 +384167580654720*x^4 +69965704049565*x^3 +3673269278420*x^2 +31330727961*x +4194304) / (x -1)^12. [Colin Barker, Feb 22 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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