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 A050772 Iterated procedure 'composite k added to sum of its prime factors reaches a prime' yields 5 skipped primes. 1

%I #16 Nov 22 2021 10:10:13

%S 18,24,25,46,57,161,203,209,288,319,323,391,736,798,837,858,928,930,

%T 1035,1088,1089,1218,1300,1376,1690,2254,2418,2478,2673,2842,2871,

%U 3045,3220,3325,3458,3510,3588,4186,4508,4617,4824,5054,5180,5248,5472,6069

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

%H Robert Israel, <a href="/A050772/b050772.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%p filter:= proc(n) local r, s, t;

%p if isprime(n) then return false fi;

%p t:= 0: s:= n;

%p do

%p r:= s;

%p t:= t + numtheory:-pi(s-1) - numtheory:-pi(r);

%p if isprime(s) then return t=5 fi;

%p if t > 5 then return false fi;

%p od;

%p end proc:

%p select(filter, [\$2..10000]); # _Robert Israel_, May 08 2020

%t 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 *)

%Y Cf. A050703, A050710.

%K nonn

%O 1,1

%A _Patrick De Geest_, Sep 15 1999

%E Offset changed to 1 by _Robert Israel_, May 08 2020

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Last modified September 9 07:24 EDT 2024. Contains 375762 sequences. (Running on oeis4.)