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%I #6 Jan 08 2018 04:51:20
%S 687,1186,1631,1906,1994,2391,3107,3687,3755,4786,5991,6155,6218,7715,
%T 7967,8306,8327,8351,9298,9731,9995,11567,12178,12938,13391,13607,
%U 13787,13863,14367,15434,15506,15578,16595,16658,16706,17039,17687,18663,19466,19631,21687
%N Take a squarefree semiprime and take the difference of its prime factors. If it is a squarefree semiprime repeat the process. Sequence lists the squarefree semiprimes that generate other squarefree semiprimes only in the first k steps of this process. Case k = 4.
%C For any pair of distinct prime numbers p and q, if p * q belongs to this sequence, then abs(p - q) belongs to A296810. - _Rémy Sigrist_, Jan 07 2018
%e 687 = 3*229, 229-3 = 226 = 2*113, 113-2 = 111 = 3*37, 37-3 = 34 = 2*17, 17-2 = 15 = 3*5 but 5-3 = 2 is not a squarefree semiprime.
%e 1186 = 2*593, 593-2 = 591 = 3*197 = 197-3 = 194 = 2*97 = 97-2 = 95 = 5*19, 19-5 = 14 = 2*7 but 7-2 = 5 is not a squarefree semiprime.
%p with(numtheory): P:=proc(n,h) local a,j,ok; ok:=1; a:=n; for j from 1 to h do if issqrfree(a) and nops(factorset(a))=2 then a:=ifactors(a)[2]; a:=a[1][1]-a[2][1]; else ok:=0; break; fi; od;if ok=1 then n; fi; end: seq(P(i,5),i=1..2*10^3);
%Y Cf. A001358, A296096, A296808, A296810.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Dec 21 2017
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