A048129 Becomes prime or 4 after exactly 7 iterations of f(x) = sum of prime factors of x.

393, 422, 614, 674, 692, 886, 889, 934, 993, 1006, 1270, 1285, 1502, 1522, 1524, 1542, 1726, 1822, 2018, 2217, 2326, 2386, 2402, 2474, 2545, 2654, 2733, 2734, 2761, 2858, 2876, 3005, 3022, 3039, 3054, 3147, 3193, 3261, 3453, 3507, 3512, 3518, 3589

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

f(x) = sum of prime factors with multiplicity, so that f(1500) = 2+2+3+5+5+5 = 22.

Programs

Mathematica

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 *)