A226218 Ending primes for n-th composite number in the iterated procedure of composite added to sum of prime factors.

23, 11, 23, 23, 17, 19, 23, 23, 47, 41, 29, 31, 47, 47, 47, 41, 71, 71, 71, 83, 47, 53, 47, 71, 59, 71, 71, 83, 59, 167, 71, 59, 149, 167, 71, 167, 83, 71, 167, 79, 89, 251, 167, 149, 149, 83, 269, 89, 167, 251, 251, 113, 239, 149, 167, 109, 127, 269, 251, 107

Offset: 1

Author

Jayanta Basu, May 31 2013

Keywords

• nonn

Comments

If we consider nonprimes instead of composite then a(1)=2. Sorted list of primes generated here are given in A050778.

Examples

			For the first composite number 4 repeated application of composite added to sum of prime factors give 4, 8, 14, 23 and so a(1)=23.
		

Crossrefs

Cf. A050703-A050710, A050778.

Programs

Mathematica

a[n_] := NestWhile[#+Total[Times@@@FactorInteger[#]]&, n, !PrimeQ[#]&]; t={}; Do[If[!PrimeQ[n], AppendTo[t, a[n]]], {n, 4, 80}]; t