Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes.

P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ...

P = 2, 5, 10, 17, 28, etc.



Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites.

C = (4), (4 + 6), (4 + 6 + 8), (4 + 6 + 8 + 9), (4 + 6 + 8 + 9 + 10), ...

C = 4, 10, 18, 27, 37, etc.



Notice that the third term of P; P3 (10) is equal to the second term of C; C2 (10);



Task
 Find and display the indices (n, m) and value of at least the first 6 terms of the sequence of numbers that are both the sum of the first n primes and the first m composites.


See also
 OEIS:A007504 - Sum of the first n primes
 OEIS:A053767 - Sum of first n composite numbers
 OEIS:A294174 - Numbers that can be expressed both as the sum of first primes and as the sum of first composites


def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] +.;
 
def task($sievesize):
  {compSums:[],
   primeSums:[],
   csum:0,
   psum:0 }
  | reduce range(2; $sievesize) as $i (.;
      if $i|is_prime
      then .psum += $i
      | .primeSums += [.psum]
      else .csum += $i
      | .compSums += [ .csum ]
      end)
  | range(0; .primeSums|length) as $i
  | .primeSums[$i] as $ps
  | (.compSums | index( $ps )) as $ix
  | select($ix >= 0)
  | "\($ps|lpad(21)) - \($i+1|lpad(21)) prime sum, \($ix+1|lpad(12)) composite sum"
;
 
task(1E5)