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%I #12 Dec 27 2019 15:52:03
%S 4,10,14,35,39,49,55,65,69,91,95,121,142,146,155,159,169,178,187,201,
%T 205,209,213,217,221,235,249,253,259,265,274,278,287,291,295,299,303,
%U 309,319,323,327,341,355,361,365,371,377,381,391,395,417,427,437,446
%N a(1) = 4; a(n) = smallest semiprime > a(n-1) such that a(n) - a(n-1) is semiprime.
%C Subsequence of semiprimes with semiprime gaps.
%H Michael De Vlieger, <a href="/A175588/b175588.txt">Table of n, a(n) for n = 1..10000</a>
%t Nest[Append[#, Block[{k = #[[-1]] + 1}, While[! AllTrue[{k, k - #[[-1]]}, PrimeOmega[#] == 2 &], k++]; k]] &, {4}, 53] (* _Michael De Vlieger_, Dec 23 2019 *)
%o (PARI) (nxt_A175588(t)=for(d=4,oo,bigomega(d)==2&&bigomega(t+d)==2&&return(t+d))); vector(99, i, t=nxt_A175588(if(i>1,t))) \\ _M. F. Hasler_, Dec 22 2019
%Y Cf. A175587 (subsequence of semiprimes with prime gaps), A001358 (semiprimes).
%K nonn
%O 1,1
%A _Zak Seidov_, Jul 17 2010
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