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A201993
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Conjectured lower bound for the number of circles of radius 1 that can be packed into a circle of radius n.
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2
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1, 2, 6, 11, 18, 26, 37, 49, 63, 79, 97, 116, 138, 161, 186, 213, 241, 272, 304, 338, 374, 412, 451, 492, 535, 580, 627, 676, 726, 778, 832, 888, 946, 1005, 1066, 1130, 1194, 1261, 1330, 1400, 1472, 1546, 1622, 1699, 1779, 1860, 1943, 2028, 2115, 2203, 2293, 2385
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OFFSET
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1,2
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COMMENTS
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Bound provided by David W. Cantrell in December 2008. It is conjectured that it is possible to find packings such that A023393(n)>=a(n) for all n. Currently (December 2011) the smallest number of circles, for which the bound is not achieved, is 507.
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LINKS
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FORMULA
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a(n) = Smallest k, such that 1 + (sqrt((4*Rho-1)^2 + 16*Rho*(k-1)) - 1) / (4*Rho) >=n with Rho = Pi/(2*sqrt(3)).
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PROG
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(PARI) for(k=2, 53, my(rho=Pi/(2*sqrt(3)), N(R)=rho*R*(R-2)+R/2+1); print1(ceil(N(k-1)), ", ")) - Hugo Pfoertner, Aug 02 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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