A050772 Iterated procedure 'composite k added to sum of its prime factors reaches a prime' yields 5 skipped primes.

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

Offset: 1

Author

Patrick De Geest, Sep 15 1999

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A050703, A050710.

Programs

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

Mathematica

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 *)

Extensions

Offset changed to 1 by Robert Israel, May 08 2020