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A050772 Iterated procedure 'composite k added to sum of its prime factors reaches a prime' yields 5 skipped primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

EXAMPLE

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.

MAPLE

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:

select(filter, [$2..10000]); # Robert Israel, May 08 2020

PROG

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 *)

CROSSREFS

Cf. A050703, A050710.

Sequence in context: A339473 A002505 A182438 * A086473 A271327 A243539

Adjacent sequences:  A050769 A050770 A050771 * A050773 A050774 A050775

KEYWORD

nonn

AUTHOR

Patrick De Geest, Sep 15 1999

EXTENSIONS

Offset changed to 1 by Robert Israel, May 08 2020

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)