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%I #28 Mar 03 2024 10:15:06
%S 4,9,14,21,26,33,38,49,62,65,82,85,122,129,134,141,146,159,166,169,
%T 206,209,214,217,254,259,262,265,278,289,302,305,334,339,346,365,382,
%U 393,398,403,422,427,446,451,454,471,478,481,542,545
%N a(1) = 4; a(n) = smallest semiprime such that a(n) - a(n-1) is an odd prime.
%C a(n) >= A175587(n).
%C First differences: 5, 5, 7, 5, 7, 5, 11, 13, 3, 17, 3, 37, 7, 5, 7, 5, 13, 7, 3, 37, 3, 5, 3, 37, 5, 3, 3, 13, 11, 13, 3, 29, 5, 7, 19, 17, 11, 5, 5, 19, 5, 19, 5, 3, 17, 7, 3, 61, 3 (all odd primes).
%H Zak Seidov, <a href="/A281314/b281314.txt">Table of n, a(n) for n = 1..1000</a>
%t NestList[(p = 3; While[2 != PrimeOmega[q = # + p], p = NextPrime[p]]; q) &, 4, 50]
%t nxt[n_]:=Module[{k=n+1},While[PrimeOmega[k]!=2||!PrimeQ[k-n]||EvenQ[k-n],k++];k]; NestList[nxt,4,50] (* _Harvey P. Dale_, Feb 14 2019 *)
%Y Cf. A001358, A017558.
%K nonn
%O 1,1
%A _Zak Seidov_, Jan 25 2017