Centered tetrahedral number

Summary

A centered tetrahedral number is a centered figurate number that represents a tetrahedron. The centered tetrahedral number for a specific n is given by

Centered tetrahedral number
Total no. of termsInfinity
Subsequence ofPolyhedral numbers
Formula
First terms1, 5, 15, 35, 69, 121, 195
OEIS index

The first such numbers are 1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ... (sequence A005894 in the OEIS).

Parity and divisibility edit

  • 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   or   is a divisor of 3.

References edit

  • Deza, E.; Deza, M. (2012). Figurate Numbers. Singapore: World Scientific Publishing. pp. 126–128. ISBN 978-981-4355-48-3.