A048130 Becomes prime or 4 after exactly 8 iterations of f(x) = sum of prime factors of x.

1257, 1556, 1774, 1982, 2566, 2649, 4249, 4405, 4497, 4645, 5086, 5169, 5286, 5317, 5462, 5574, 6070, 6074, 6382, 6518, 7064, 7149, 7197, 7284, 7694, 7813, 7947, 8043, 8193, 8593, 8605, 8852, 8894, 8902, 8998, 9057, 9182, 9562, 9575, 10232, 10326

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.

Getting 4 is rare (only 1 such instance in the first 5,000 terms). - Harvey P. Dale, Nov 19 2023

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..5000

Programs

Mathematica

fi[n_]:=Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]]; bpQ[n_]:=Boole[PrimeQ[NestList[ fi[#]&,n,8]]] =={0,0,0,0,0,0,0,0,1}||Nest[fi[#]&,n,7]==4; Select[Range[11000],bpQ] (* Harvey P. Dale, Nov 19 2023 *)