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%I #7 Jan 26 2021 11:14:34
%S 7,23,113,139,199,211,293,317,523,691,887,1039,1069,1129,1259,1327,
%T 1381,1637,1669,1759,1831,1933,1951,2113,2179,2297,2311,2423,2477,
%U 2503,2557,2593,2633,2861,2971,3089,3137,3229,3271,3433,3739,3889,3947,3967,4159,4177,4297,4463,4523,4733,4759,4831
%N Primes p such that, if q is the next prime after p, the sum of prime factors (with multiplicity) of the composites between p and q is at least p+q.
%H Robert Israel, <a href="/A340889/b340889.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 23 is in the sequence because between primes 23 and 29 we have 24 = 2^3*3, 25 = 5^2, 26 = 2*13, 27 = 3^3, 28 = 2^2*7, and 3*2+3+2*5+2+13+3*3+2*2+7 = 54 >= 23 + 29.
%p count:= 0: R:= NULL:
%p p:= 2:
%p while count < 100 do
%p t:= 0:
%p for q from p+1 while not isprime(q) do
%p t:= t + add(s[1]*s[2],s=ifactors(q)[2])
%p od;
%p if t >= p+q then
%p count:= count+1; R:= R, p;
%p fi;
%p p:= q;
%p od:
%p R;
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 25 2021
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