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%I #11 Mar 30 2012 18:52:54
%S 1,1,1,1,5,7,5,1,17,1,23,5,5,1,11,19,5,5,47,13,29,7,1,11,29,19,5,103,
%T 107,11,5,137,23,13,7,17,43,7,59,13,1,41,71,43,31,11,17,11,19,31,67,5,
%U 139,283,41,149,13,313,23,13,37,13,347,29,11,71,17,373,7,11,13,397,17,1,443,7,113,13,31,467,11,5,13,11,271,181,11,37,7,281,113,577,17,7,59,593,199,17,157,13
%N Maximal prime divisor of the average of the twin prime pairs, different from 2 and 3. In case of maximal prime divisor is 2 or 3, then a(n)=1.
%C 78 from the first 100 terms are first or second members of twin pairs and only 12 are not. In a natural supposition that for large prime terms the latter should be in the majority, there are reasons to assume that the number N for which it occurs for the first time is very large.
%C The average of a twin-prime pair is the same as 1 + the lower twin prime, whose largest prime factor is tabulated in A060210.
%t s = Plus @@@ Select[ Partition[ Prime@ Range@ 350, 2, 1], #[[1]] + 2 == #[[2]] &]; f[n_] := Max[First /@ FactorInteger@ n] /. {2 -> 1, 3 -> 1}, f /@ s
%Y Cf. A178456, A178527, A001359
%K nonn
%O 1,5
%A _Vladimir Shevelev_, Dec 25 2010
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