A391189 a(n) = least integer m such that concatenating n distinct nonzero squares <= m^2 in ascending order yields a perfect square.

1, 3, 6, 10, 14, 29, 29, 70

Offset

1,2

Comments

a(n) <= square root of the largest of the n squares that was used to construct A391022(n).

Links

Table of n, a(n) for n=1..8.

Example

Case n=2: Squares <= 3^2 = 9 are 1,4,9.
Concatenating 4 and 9 gives 49, which is 7^2. Thus a(2) = 3.

Prog

(Python)
from math import isqrt
from itertools import combinations, count
def is_square(n): return isqrt(n)**2 == n
def a(n):
    squares = [str(i*i) for i in range(1, n)]
    for m in count(n):
        mm = str(m**2)
        for c in combinations(squares, n-1):
            if is_square(s:=int("".join(c)+mm)):
                return m # use s to obtain the concatenation of squares
        squares.append(mm)
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Dec 03 2025

Crossrefs

Cf. A019521, A391022.

Sequence in context: A049989 A330258 A197056 * A379675 A104619 A194037

Adjacent sequences: A391186 A391187 A391188 * A391190 A391191 A391192

Keyword

nonn,base,more

Author

Jean-Marc Rebert, Dec 02 2025

Status

approved