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.

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

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

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

Sequence in context: A096327 A267805 A154113 * A053706 A137367 A267926

Adjacent sequences: A340886 A340887 A340888 * A340890 A340891 A340892

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 25 2021

Status

approved