A352738 Squares in A086849.

16, 64, 441, 729, 81796, 1320201, 2729104, 44488900, 34614230401, 209453590921, 752884200721, 5054227881921, 8106120765625, 14483961408400, 433446375390625, 530837821446724, 1270089068379481, 1383781075827264, 4819866587217081, 7032375864510896656

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 30 2022

Keywords

• nonn

Comments

Squares that are partial sums of A000037.

Examples

			a(2) = 64 is a term because 64 = 8^2 = 2+3+5+6+7+8+10+11+12 is a square and the sum of the nonsquares up to 12.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..23

Crossrefs

Cf. A000037, A086849.

Programs

Maple

R:= NULL: count:= 0:
s:= 0:
for n from 1 do
  if issqr(n) then next fi;
  s:= s+n;
  if issqr(s) then
    count:= count+1;
    R:= R,s;
    if count = 19 then break fi
  fi;
od:
R;

Python

from itertools import islice
def A352738_gen(): # generator of terms
    c, k, ks, m, ms = 0, 1, 2, 1, 1
    while True:
        for n in range(ks,ks+2*k):
            c += n
            if c == ms:
                yield c
            elif c > ms:
                ms += 2*m+1
                m += 1
        ks += 2*k+1
        k += 1
A352738_list = list(islice(A352738_gen(),10)) # Chai Wah Wu, Mar 31 2022

Extensions

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