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%I #7 Jul 11 2014 16:20:04
%S 393,422,614,674,692,886,889,934,993,1006,1270,1285,1502,1522,1524,
%T 1542,1726,1822,2018,2217,2326,2386,2402,2474,2545,2654,2733,2734,
%U 2761,2858,2876,3005,3022,3039,3054,3147,3193,3261,3453,3507,3512,3518,3589
%N Becomes prime or 4 after exactly 7 iterations of f(x) = sum of prime factors of x.
%C f(x) = sum of prime factors with multiplicity, so that f(1500) = 2+2+3+5+5+5 = 22.
%t spf[n_]:=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[n]]]; pf7Q[ n_]:= Module[ {lst=NestList[spf,n,7]},NoneTrue[Most[lst], PrimeQ] && !MemberQ[Most[lst],4]&&(PrimeQ[Last[lst]]||Last[lst]==4)]; Select[Range[ 3600],pf7Q] (* _Harvey P. Dale_, Jul 11 2014 *)
%K nonn
%O 1,1
%A _David W. Wilson_
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