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.

A036102 Centered cube numbers: (n+1)^24 + n^24.

Original entry on oeis.org

1, 16777217, 282446313697, 281757406247137, 59886119752101281, 4797985983097007521, 196319612718888031297, 4913947714250211628097, 84488809559742155077057, 1079766443076872509863361
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

Can never be prime, as a(n) = (2n^8 + 8n^7 + 28n^6 + 56n^5 + 70n^4 + 56n^3 + 28n^2 + 8n + 1) * (n^16 + 8n^15 + 92n^14 + 504n^13 + 1750n^12 + 4312n^11 + 7980n^10 + 11432n^9 + 12869n^8 + 11440n^7 + 8008n^6 + 4368n^5 + 1820n^4 + 560n^3 + 120n^2 + 16n + 1). [Jonathan Vos Post, Aug 28 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. A010812, A036100, A036101.

Programs

  • Magma
    [(n+1)^24+n^24: n in [0..20]]; // Vincenzo Librandi, Aug 28 2011
  • Mathematica
    Total/@Partition[Range[0,10]^24,2,1] (* Harvey P. Dale, Nov 23 2013 *)

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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