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A226218
Ending primes for n-th composite number in the iterated procedure of composite added to sum of prime factors.
0
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
1,1
COMMENTS
If we consider nonprimes instead of composite then a(1)=2. Sorted list of primes generated here are given in A050778.
EXAMPLE
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.
MATHEMATICA
a[n_] := NestWhile[#+Total[Times@@@FactorInteger[#]]&, n, !PrimeQ[#]&]; t={}; Do[If[!PrimeQ[n], AppendTo[t, a[n]]], {n, 4, 80}]; t
CROSSREFS
KEYWORD
nonn
AUTHOR
Jayanta Basu, May 31 2013
STATUS
approved