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A050706
Composites c that reach a prime after 2 iterations of c-> c+sum of prime factors of c.
6
8, 9, 18, 22, 24, 25, 36, 39, 40, 54, 78, 80, 81, 91, 94, 99, 104, 106, 115, 119, 121, 122, 126, 134, 138, 142, 144, 146, 152, 159, 164, 170, 174, 187, 189, 214, 218, 219, 226, 228, 231, 232, 237, 250, 258, 262, 264, 265, 266, 272, 274, 276, 280, 282, 288, 289
OFFSET
1,1
EXAMPLE
226 is a term:
Iteration 1: 226 = 2*113 so 226 + (2+113) = 226 + 115 = 341 and composite.
Iteration 2: 341 = 11*31 so 341 + (11+31) = 341 + 42 = 383 and prime.
MATHEMATICA
aQ[n_]:=PrimeQ[Nest[#+Total[Times@@@FactorInteger[#]]&, n, 2]]; Select[Range[289], !PrimeQ[#]&&aQ[#]&] (* Jayanta Basu, May 31 2013 *)
PROG
(Magma) f:=func<n|n+(&+[j[1]*j[2]: j in Factorization(n)]) >; a:=[]; for k in [4..300] do if not IsPrime(k) and not IsPrime(f(k)) and IsPrime(f(f(k))) then Append(~a, k); end if; end for; a; // Marius A. Burtea, Oct 18 2019
KEYWORD
nonn
AUTHOR
Patrick De Geest, Aug 15 1999
EXTENSIONS
Name edited by Michel Marcus, Oct 18 2019
STATUS
approved