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A291465
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a(n) is the least m >= n for which the complete bipartite graph K_{m,n} has a prime labeling.
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5
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1, 2, 4, 9, 14, 25, 36, 45, 52, 61, 62, 89, 90, 95, 98, 123, 140, 155, 162, 171, 172, 177, 216, 217, 226, 243, 244, 255, 264, 283, 318, 321, 340, 345, 374, 383, 384, 395, 400, 403, 422, 449, 456, 465, 478, 531, 546, 551, 552, 557, 562, 567, 594, 599, 604, 605
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OFFSET
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1,2
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COMMENTS
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A prime labeling of K_{m,n} is a pair of sets A and B whose union is {1,2,...,m+n} such that |A| = m, |B| = n, and gcd(a,b) = 1 for all a in A and b in B. For an equivalent definition, the data above, and the formula below involving R_{n-1}, see Berliner, Dean, Hook, Marr, Mbirika (2016) Section 3.2.
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LINKS
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FORMULA
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n+1 <= a(n) <= R_{n-1} - n for n > 2, where R_{n-1} is a Ramanujan prime A104272.
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EXAMPLE
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A = {1,3} and B = {2,4} is a prime labeling of K_{2,2}, so a(2) = 2.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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