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%I #6 Oct 15 2013 22:31:50
%S 2,4,6,8,14,10,18,22,34,16,26,32,38,50,62,54,58,46,64,86,82,74,98,106,
%T 94,118,122,128,146,134,142,162,178,158
%N Each a(n) is a difference of suitable consecutive primes, a(n)=Prime[1+A080376(n)]-Prime[A080376(n)]. a(n+1) is the smallest prime-difference [from A001223] which has prime-factor not present in previous terms or was present but at lower power.
%e 18 is the 7th term:in first-6th ones {2,4,6,8,14,10} 3 does not occur with power 2 unlike in 18; 22 is the 8th term: in first-7th terms 11 is not a prime factor unlike 22. several even numbers do not arise in this sequence, e.g.:12,20,36,48, etc..
%t s=1; Do[s1=s; s=LCM[s, d=Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[d]], {n, 1, 10000000}]
%Y Cf. A001223, A080374-A080376.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 27 2003
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