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A109226 If g(x) is the x-th prime gap, then g(a(n)) are prime gaps which are greater than the sum of the preceding two prime gaps.

%I A109226 #6 Oct 13 2019 09:48:31
%S A109226 30,34,42,46,53,61,62,66,91,97,99,106,114,121,137,145,146,150,154,162,
%T A109226 172,175,180,189,203,214,217,221,232,239,250,258,259,263,266,274,278,
%U A109226 289,293,297,304,309,316,319,324,331,334,335,338,342,344,350,357,360
%N A109226 If g(x) is the x-th prime gap, then g(a(n)) are prime gaps which are greater than the sum of the preceding two prime gaps.
%e A109226 34 is in the sequence because if g(34) = 35th_prime - 34th_prime = 149 - 139 = 10 and g(33) = 34th_prime - 33rd_prime = 139 - 137 = 2 and g(32) = 33rd_prime - 32nd_prime = 137 - 131 = 6, then g(34) > g(33) + g(32) or 10 > 2 + 6
%t A109226 g[n_] := Prime[n + 1] - Prime[n]; Select[Range[3, 360], g[ # ] > g[ # - 1] + g[ # - 2] &] (* _Ray Chandler_, Aug 23 2005 *)
%Y A109226 Cf. A001223, A066495.
%K A109226 nonn
%O A109226 1,1
%A A109226 _Ray G. Opao_, Aug 19 2005
%E A109226 Extended by _Ray Chandler_, Aug 23 2005