Centered tetrahedral number
Appearance
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Total no. of terms | Infinity |
---|---|
Subsequence of | Polyhedral numbers |
Formula | |
First terms | 1, 5, 15, 35, 69, 121, 195 |
OEIS index |
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A centered tetrahedral number is a centered figurate number that represents a tetrahedron. The centered tetrahedral number for a specific n is given by
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.