A296814 - OEIS

%I #4 Jan 06 2018 22:04:18

%S 28738,137042,373763,384767,662426,686627,775595,888227,896498,919115,

%T 1216311,1599578,2022119,2027195,2218978,2234018,2276543,2307491,

%U 2375522,2625351,2920067,3202863,3329891,3457887,3568151,3904634,3917882,4359491,4468634,4710863,4773347

%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 = 7.

%e 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,8),i=1..2*10^3);

%Y Cf. A001358, A296096, A296808.

%K nonn,easy

%O 1,1

%A _Paolo P. Lava_, Dec 21 2017