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%I #8 Dec 13 2015 01:33:57
%S 4,6,8,12,18,24,30,38,48,60,72,84,98,114,132,150,168,192,224,258,294,
%T 332,374,420,468,522,578,642,710,788,878,968,1062,1164,1278,1400,1524,
%U 1658,1802,1950,2100,2252,2412,2580,2750,2928,3110,3300,3492,3692,3908
%N a(n) is a composite number at the start of an interval of consecutive integers, ending in a prime, and non-overlapping with and at least as long as the interval addressed by a(n-1).
%C Non-overlapping intervals of the integers of nondecreasing length, starting with a composite number and ending with a prime number, define an intermediate table (as below), the first column of which defines the sequence.
%C 4, 5
%C 6, 7
%C 8, 9, 10, 11
%C 12, 13, 14, 15, 16, 17
%C 18, 19, 20, 21, 22, 23
%C 24, 25, 26, 27, 28, 29
%C 30, 31, 32, 33, 34, 35, 36, 37
%C 38, 39, 40, 41, 42, 43, 44, 45, 46, 47
%C 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59
%C 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
%F a(n) = 1 + A070866(n+1). - _R. J. Mathar_, Jun 07 2010
%t PrimeNext[n_]:=Module[{k},k=n+1;While[ !PrimeQ[k],k++ ];k]; d=0;p=2;lst={}; Do[d=PrimeNext[p+d]-p;p=p+=d;d--;AppendTo[lst,p+1],{n,0,5!}];lst
%Y Cf. A070865, A178547.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 29 2010
%E Definition rephrased by _R. J. Mathar_, Jun 07 2010
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