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A050706
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Composites c that reach a prime after 2 iterations of c-> c+sum of prime factors of c.
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6
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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aQ[n_]:=PrimeQ[Nest[#+Total[Times@@@FactorInteger[#]]&, n, 2]]; Select[Range[289], !PrimeQ[#]&&aQ[#]&] (* Jayanta Basu, May 31 2013 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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