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A016837
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Primes reached after k iterations of sum of n and its prime divisors = t (where t replaces n in each iteration).
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1
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2, 23, 11, 23, 17, 11, 17, 23, 23, 17, 47, 19, 41, 23, 23, 47, 53, 41, 59, 29, 31, 53, 71, 47, 47, 41, 71, 71, 89, 71, 167, 83, 47, 53, 47, 71, 113, 59, 71, 71, 269, 83, 131, 59, 167, 71, 167, 59, 149, 167, 71, 167, 191, 83, 71, 127, 251, 149, 179, 239, 227, 263
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Patrick asked what composite would produce 666 or 313 iterations. Carlos has also been working on the problem and asks if there is a run of 3 primes produced by consecutive composites. So original idea belongs to Patrick. This sequence was calculated by Enoch.
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 940
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FORMULA
| Factor n, add n and its prime divisors. Sum = t, t replaces n, repeat until a prime is produced.
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EXAMPLE
| a(4)=4. 4=2*2, so 4+2+2=8. 8=2*2*2 so 8+2+2+2=14. 14=2*7 so 14+2+7=23, prime in 3 iterations.
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CROSSREFS
| A018845.
Sequence in context: A104644 A158992 A128365 * A153654 A153656 A084323
Adjacent sequences: A016834 A016835 A016836 * A016838 A016839 A016840
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KEYWORD
| easy,nonn
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AUTHOR
| Enoch Haga, Carlos B. Rivera F., Patrick De Geest (Enokh(AT)comcast.net, crivera(AT)ux1.sci.net.mx, pdg(AT)worldofnumbers.com)
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