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

1,1

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

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 *)

Crossrefs

Cf. A050703, A050710.

Sequence in context: A361627 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