Some Distribution Numbers of the Triangular Association Scheme
نویسندگان
چکیده
منابع مشابه
Some New Properties of Balancing Numbers and Square Triangular Numbers
A number N is a square if it can be written as N = n2 for some natural number n; it is a triangular number if it can be written as N = n(n + 1)/2 for some natural number n; and it is a balancing number if 8N2 +1 is a square. In this paper, we study some properties of balancing numbers and square triangular numbers.
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have infinitely many solutions. If the well known hypothesis about prime twins is true, that is, if the equation pn+i—pn — 2 has infinitely many solutions, (1) and (2) of course are trivially satisfied. The first inequality of (2) is inserted only for the sake of completeness. I t follows from the well known fact that lim sup (pn+i—pn) = °° (since n\+2, n\+3, • • • , » ! + » are all composite)....
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1. BALANCING NUMBERS We call an Integer n e Z a balancing number if 1+ 2+ --+ (»l ) = (w + l) + (w + 2) +••• + (» + >•) (1) for some r e Z. Here r is called the balancer corresponding to the balancing number n. For example, 6, 35, and 204 are balancing numbers with balancers 2, 14, and 84, respectively. It follows from (1) that, if n is a balancing number with balancer r, then n2^(n + r)(n + r ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1988
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(88)80021-0