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

1,1

Comments

Squares that are partial sums of A000037.

Links

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

Example

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.

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;

Prog

(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

Crossrefs

Cf. A000037, A086849.

Sequence in context: A255661 A073718 A230970 * A061449 A168091 A181208

Adjacent sequences: A352735 A352736 A352737 * A352739 A352740 A352741

Keyword

nonn

Author

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

Extensions

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

Status

approved