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a(0)=3; for n>0, a(n) = smallest odd prime not occurring earlier in the sequence such that a(n-1)+a(n) is a multiple of n.
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%I #13 Sep 16 2015 12:58:52

%S 3,5,7,11,13,17,19,23,41,31,29,37,47,83,43,107,53,151,101,89,71,97,79,

%T 59,61,139,173,313,163,127,113,73,311,283,193,157,131,239,103,443,197,

%U 541,257,431,229,401,887,241,191,397,353,463,109,421,227,433,631,167

%N a(0)=3; for n>0, a(n) = smallest odd prime not occurring earlier in the sequence such that a(n-1)+a(n) is a multiple of n.

%C Is this sequence infinite and, if so, is it a permutation of the odd primes?

%C An analog of A134204, but using only the odd primes.

%H Olivier GĂ©rard, <a href="/A131261/b131261.txt">Table of n, a(n) for n = 0..1000</a>

%t a = {3}; For[n = 1, n < 60, n++, i = 2; While[Length[Intersection[{Prime[i]}, a]] == 1 || Not[Mod[a[[ -1 ]] + Prime[i], n] == 0], i++ ]; AppendTo[a, Prime[i]]]; a (* _Stefan Steinerberger_, Oct 30 2007 *)

%Y Cf. A134204.

%K nonn

%O 0,1

%A _David Applegate_, Oct 26 2007