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a(1) = 1; for n>1, a(n) is the smallest positive integer such that the continued fraction [a(1),a(2),a(3),...,a(n)] has numerator divisible by n.
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%I #8 Apr 09 2014 10:15:59

%S 1,1,1,2,4,2,7,2,7,10,5,10,4,2,7,2,9

%N a(1) = 1; for n>1, a(n) is the smallest positive integer such that the continued fraction [a(1),a(2),a(3),...,a(n)] has numerator divisible by n.

%e a(5) = 4 because 4 is the smallest positive integer m such that the continued fraction [1,1,1,2,m] has numerator divisible by 5.

%e 1 + 1/(1 + 1/(1 + 1/(2 + 1/4))) = 35/22 and 35 is divisible by 5.

%e [1,1,1,2,4,2,7,2,7,10,5,10] equals 4878960/3065089 and 12 divides 4878960.

%K nonn,fini,full

%O 1,4

%A _Leroy Quet_, Sep 23 2005

%E Completed by _Hans Havermann_, Sep 23 2005. Rechecked Oct 23, 2005