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 1-2 of 2 results.

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

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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 *)

A036101 Centered cube numbers: (n+1)^23 + n^23.

Original entry on oeis.org

1, 8388609, 94151567435, 70462887356491, 11991297699255789, 801651152008680941, 28158477563134519159, 617664557698786568055, 9453233930011206747641, 108862938119652501095929
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Can never be prime, as a(n) = (2n + 1) * (n^22 + 11n^21 + 121n^20 + 825n^19 + 4015n^18 + 14817n^17 + 43065n^16 + 101046n^15 + 194634n^14 + 311278n^13 + 416394n^12 + 467842n^11 + 442118n^10 + 350974n^9 + 233108n^8 + 128603n^7 + 58277n^6 + 21335n^5 + 6157n^4 + 1349n^3 + 211n^2 + 21n + 1). a(1) is semiprime (A001358). [Jonathan Vos Post, Aug 28 2011]

Examples

			a(2) = 1^23 + (1+1)^23 = 8388609 = 3 * 2796203, which is semiprime.

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. A010811, A036099, A036100.

Programs

  • Magma
    [(n+1)^23+n^23: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
  • Mathematica
    Total/@Partition[Range[0,20]^23,2,1] (* Harvey P. Dale, Nov 02 2023 *)
Showing 1-2 of 2 results.

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

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