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%I #7 Jan 06 2018 22:04:28
%S 373763,2276543,4710863,5840138,6108239,6443183,6458303,6983939,
%T 7136306,7861439,7997915,8212934,9861599,11261531,11834786,11921123,
%U 12204659,13520063,13851443,15236327,15827978,17312258,17632739,18661922,19432739,19523195,19793603,20301986,20335439,20441459
%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 = 8.
%e 373763 = 13*28751, 28751-13 = 28738 = 2*14369, 14369-2 = 14367 = 3*4789, 4789-3 = 4786 = 2*2393, 2393-2 = 2391 = 3*797, 797-3 = 794 = 2*397, 397-2 = 395 = 5*79 = 79-5 = 74 = 2*37, 37-2 = 35 = 5*7 but 7-5 = 2 is not a squarefree semiprime.
%e 2276543 = 79*28817, 28817-79 = 28738 = 2*14369, 14369-2 = 14367 = 3*4789, 4789-3 = 4786 = 2*2393, 2393-2 = 2391 = 3*797, 797-3 = 794 = 2*397, 397-2 = 395 = 5*79 = 79-5 = 74 = 2*37, 37-2 = 35 = 5*7 but 7-5 = 2 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,9),i=1..10^8);
%Y Cf. A001358, A296096, A296808.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Dec 21 2017