A050707 Composites c that reach a prime after 3 iterations of c -> c + sum of prime factors of c.

4, 16, 27, 28, 30, 42, 76, 87, 92, 95, 108, 114, 120, 124, 128, 133, 136, 147, 148, 154, 172, 196, 202, 204, 216, 222, 238, 242, 243, 244, 245, 255, 256, 260, 285, 286, 292, 308, 310, 325, 338, 340, 342, 350, 386, 412, 418, 422, 423, 426, 435, 440, 458, 464

Offset: 1

Author

Patrick De Geest, Aug 15 1999

Keywords

• nonn

Examples

			204 is a term:
Iteration 1: 204 = 2*2*3*17 so 204 + (2+2+3+17) = 204 + 24 = 228 and composite.
Iteration 2: 228 = 2*2*3*19 so 228 + (2+2+3+19) = 228 + 26 = 254 and composite.
Iteration 3: 254 = 2*127 so 254 + (2+127) = 254 + 129 = 383 and prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1001 [offset shifted by _Georg Fischer_, Oct 29 2019]

Crossrefs

Cf. A050703, A050704, A050705, A050706, A050708, A050709, A050710.

Programs

Magma

f:=func; a:=[]; for k in [4..500] do if not IsPrime(k) and not IsPrime(f(k)) and not IsPrime(f(f(k))) and IsPrime(f(f(f(k)))) then Append(~a,k); end if; end for; a; // Marius A. Burtea, Oct 17 2019

Mathematica

nxt[n_]:=Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[n]]]+n; Select[ Range[500],PrimeQ[NestList[nxt,#,3]]=={False,False,False,True}&] (* Harvey P. Dale, Feb 23 2014 *)

Extensions

Name edited by Michel Marcus, Oct 17 2019