A343724 a(n) is the smallest n-digit square with all digits even.

0, 64, 400, 4624, 26244, 228484, 2022084, 20268004, 202208400, 2006860804, 20220840000, 200084446864, 2002004266084, 20000286620224, 200080402620484, 2000028662022400, 20000086482842244, 200002866202240000, 2000008648284224400, 20000246442286866064

Offset

1,2

Comments

From Robert G. Wilson v, May 20 2021: (Start)

The square root of any term is == {0, 2, 8} (mod 10).

Other than 1 and 9, there are no squares which contain only odd digits.

(End)

Links

Chai Wah Wu, Table of n, a(n) for n = 1..61 (terms for n = 1..40 from Robert G. Wilson v)

Mathematica

a[n_] := Block[{k = Floor[ Sqrt[10^n/5]]}, If[OddQ@k, k--]; While[ Union[ EvenQ[ IntegerDigits[ k^2]]] != {True}, k += 2]; k^2]; Array[ a, 20] (* Robert G. Wilson v, May 20 2021 *)

Prog

(Python 3.8+)
from math import isqrt
def A343724(n):
    if n == 1: return 0
    m = isqrt(2*10**(i-1))+1
    m += m % 2
    k = m**2
    s = set('02468')
    while not set(str(k)) <= s:
        m += 2
        k += 4*(m-1)
    return k # Chai Wah Wu, May 20 2021

Crossrefs

Cf. A030098, A343725.

Sequence in context: A249984 A221598 A017618 * A231841 A184773 A184765

Adjacent sequences: A343721 A343722 A343723 * A343725 A343726 A343727

Keyword

nonn,base

Author

Jon E. Schoenfield, May 19 2021

Status

approved