

A340889


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.


1



7, 23, 113, 139, 199, 211, 293, 317, 523, 691, 887, 1039, 1069, 1129, 1259, 1327, 1381, 1637, 1669, 1759, 1831, 1933, 1951, 2113, 2179, 2297, 2311, 2423, 2477, 2503, 2557, 2593, 2633, 2861, 2971, 3089, 3137, 3229, 3271, 3433, 3739, 3889, 3947, 3967, 4159, 4177, 4297, 4463, 4523, 4733, 4759, 4831
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OFFSET

1,1


LINKS



EXAMPLE

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.


MAPLE

count:= 0: R:= NULL:
p:= 2:
while count < 100 do
t:= 0:
for q from p+1 while not isprime(q) do
t:= t + add(s[1]*s[2], s=ifactors(q)[2])
od;
if t >= p+q then
count:= count+1; R:= R, p;
fi;
p:= q;
od:
R;


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



