A351855 Partial sums of nonsquares that are partial sums of nonprimes.

5, 64, 506, 64325, 268723, 480129, 6282620, 64548862, 9657523883, 13480852825, 29766135708, 105223301080, 519861666225, 851245744041, 1378216791896, 581522966976875, 583298551668358, 885441628670251, 1651966084813205, 16868988672306046, 17170433482837259

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 31 2022

Keywords

• nonn

Examples

			a(2) = 64 is a term because 64 = 1+4+6+8+9+10+12+14 = 2+3+5+6+7+8+10+11+12 is the sum of the first 8 nonprimes and the sum of the first 9 nonsquares.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..26

Crossrefs

Intersection of A051349 and A086849.

Programs

Maple

i:= 0: j:= 0: s:= 0: t:= 0:
R:= NULL: count:= 0:
while count < 13 do
  if s <= t then
     i:= i+1;
     if not issqr(i) then
       s:= s+i;
       if s=t then R:= R,s; count:= count+1 fi;
     fi
  else
     j:= j+1;
     if not isprime(j) then
       t:= t+j;
       if s=t then R:= R,t; count:= count+1 fi;
     fi
  fi
od:
R;

Python

from itertools import islice
from sympy import nextprime
def A351855_gen(): # generator of terms
    c, k, ks, m, p, q = 0, 1, 2, 1, 4, 5
    while True:
        for n in range(ks,ks+2*k):
            c += n
            if c == m:
                yield c
            else:
                while c > m:
                    m += p
                    p += 1
                    if p == q:
                        q = nextprime(q)
                        p += 1
        ks += 2*k+1
        k += 1
A351855_list = list(islice(A351855_gen(),20)) # Chai Wah Wu, Apr 04 2022

Extensions

a(20)-a(21) from Jon E. Schoenfield, Mar 31 2022