Английская Википедия:Centered tetrahedral number

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Шаблон:No footnotes Шаблон:Infobox integer sequence A centered tetrahedral number is a centered figurate number that represents a tetrahedron. The centered tetrahedral number for a specific n is given by

<math>(2n+1)\times{(n^2+n+3) \over 3}</math>

The first such numbers are 1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ... Шаблон:OEIS.

Parity and divisibility

  • Every centered tetrahedral number is odd.
  • Every centered tetrahedral number with an index of 2, 3 or 4 modulo 5 is divisible by 5.
  • The only prime centered tetrahedral number is 5. We only need to check when either <math>2n+1</math> or <math>n^2+n+3</math> is a divisor of 3.

References

Шаблон:Figurate numbers Шаблон:Classes of natural numbers


Шаблон:Num-stub