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Greatest numerator of the remainder in a reciprocal expansion of 1.
1

%I #7 Mar 30 2012 17:26:50

%S 1,1,1,5,59,4951,9770455,31950134954551

%N Greatest numerator of the remainder in a reciprocal expansion of 1.

%C Conjecture: in the "extremal" expansion x_i = A000058(i) for i=1..n-3.

%F Let 1 = 1/x_1 + ... + 1/x_{n-1} + p/q, where 1/x_1>=...>=1/x_{n-1}>=p/q and (p, q)=1. a(n) = maximal p over all such expansions. Corresponded denominators sequence is A091458.

%e a(7) = 9770455 because 1 = 1/2 + 1/3 + 1/7 + 1/43 + 1/5413 + 1/5419 + 9770455/52975482882 and there is no expansion with larger numerator of the remainder.

%Y Cf. A091458, A000058.

%K frac,hard,nonn,more

%O 1,4

%A _Max Alekseyev_, Jan 11 2004