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A050772
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Iterated procedure 'composite k added to sum of its prime factors reaches a prime' yields 5 skipped primes.
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1
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18, 24, 25, 46, 57, 161, 203, 209, 288, 319, 323, 391, 736, 798, 837, 858, 928, 930, 1035, 1088, 1089, 1218, 1300, 1376, 1690, 2254, 2418, 2478, 2673, 2842, 2871, 3045, 3220, 3325, 3458, 3510, 3588, 4186, 4508, 4617, 4824, 5054, 5180, 5248, 5472, 6069
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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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18 is a term because 18 + (2+3+3) = 26 + (2+13) = ending prime 41. Between 18 and 41 one finds 5 primes 19, 23, 29, 31 and 37.
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MAPLE
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filter:= proc(n) local r, s, t;
if isprime(n) then return false fi;
t:= 0: s:= n;
do
r:= s;
s:= s + add(p[1]*p[2], p=ifactors(s)[2]);
t:= t + numtheory:-pi(s-1) - numtheory:-pi(r);
if isprime(s) then return t=5 fi;
if t > 5 then return false fi;
od;
end proc:
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MATHEMATICA
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ok[n_] := CompositeQ[n] && Block[{k=n, p = NextPrime[n, 6]}, While[k < p, k += Total[ Times @@@ FactorInteger[k]]]; k == p]; Select[Range@ 6069, ok] (* Giovanni Resta, May 08 2020 *)
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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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