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%I #6 Dec 05 2013 19:55:38
%S 3,5,7,13,37,31,23,17,53,11,251,29,79,43,73,61,97,67,107,173,59,103,
%T 199,163,7,1,149,47,101,509,89,151,283,229,271,211,109,257,113,269,
%U 157,241,331,83,389,41,313,1543,19,307,463,373,277,811,457,137,191,419,311,197
%N a(n) is the smallest odd prime such that (1) a(n) doesn't already appear in the sequence; (2) the n-th partial sum is divisible by n; and (3) the n-th partial sum is relatively prime to n+1.
%C Condition (3) is needed to ensure that a(n+1) exists.
%e a(5)=37: The 4th partial sum is 28. 7 is the smallest odd prime that satisfies (2) (28+7=35), but 7 has already been used. 17 satisfies (1) and (2) (28+17=45), but 45+a(6) must be a multiple of 6 and the only odd prime satisfying that requirement is 3, which has already been used. 37 works (28+37=65).
%K nonn,easy
%O 1,1
%A _Amarnath Murthy_, Sep 24 2002
%E Edited by _David Wasserman_, Jun 27 2003
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