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

1,1

Links

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

Example

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.

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;

Prog

(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

Crossrefs

Intersection of A051349 and A086849.

Sequence in context: A193184 A180787 A222455 * A178295 A054937 A302993

Adjacent sequences: A351852 A351853 A351854 * A351856 A351857 A351858

Keyword

nonn

Author

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

Extensions

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

Status

approved