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triangular number counting function
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(Definition)
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For a given nonnegative number $x$ , the triangular number counting function counts how many triangular numbers are not greater than $x$ . The formula is simple: $$\lfloor \frac{-1 + \sqrt{8x + 1}}{2} \rfloor ,$$ in sharp contrast to the lack of a formula for the prime counting function $\pi(x)$ . If one accepts 0 as a triangular number, the formula easily accommodates this by the mere addition of 1 after flooring the fraction.
- 1
- Zhi-Wei Sun, ``On Sums of Primes and Triangular Numbers'' ArXiv preprint, 10 April (2008): 1
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"triangular number counting function" is owned by PrimeFan.
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Cross-references: fraction, addition, prime counting function, simple, formula, triangular numbers, number
There is 1 reference to this entry.
This is version 2 of triangular number counting function, born on 2008-05-10, modified 2008-05-13.
Object id is 10576, canonical name is TriangularNumberCountingFunction.
Accessed 587 times total.
Classification:
| AMS MSC: | 11A25 (Number theory :: Elementary number theory :: Arithmetic functions; related numbers; inversion formulas) |
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Pending Errata and Addenda
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