A343725 -id:A343725 - cp's OEIS frontend

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

Jon E. Schoenfield, May 19 2021

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)

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

Cf. A030098, A343725.

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 *)

A343726 Squares with exactly one even digit.

Original entry on oeis.org

0, 4, 16, 25, 36, 49, 81, 121, 169, 196, 361, 529, 576, 729, 961, 1156, 1369, 1521, 1936, 3136, 3721, 3969, 5329, 5776, 5929, 7396, 7569, 7921, 15129, 15376, 17161, 17956, 19321, 31329, 35721, 51529, 53361, 57121, 59536, 97969, 111556, 113569, 119716, 131769

Offset: 1

Jon E. Schoenfield, May 19 2021

The even digit is always one of the last two digits.

The only squares with no digits even are the one-digit odd squares 1 and 9.

Jianing Song, Table of n, a(n) for n = 1..10000

Cf. A000290, A030098, A118070, A343724, A343725.

q:= n-> (l-> is(add(i mod 2, i=l)=nops(l)-1))(convert(n, base, 10)):
select(q, [i^2$i=0..400])[];  # Alois P. Heinz, May 22 2021

Select[Range[0, 400]^2, Count[IntegerDigits[#], ?EvenQ] == 1 &] (* _Amiram Eldar, May 21 2021 *)

isA343726(n) = if(issquare(n) && (n!=0), my(d=digits(n)); #d - vecsum(d%2) == 1, n==0) \\ Jianing Song, May 22 2021

def ok(sq): return sum(d in "02468" for d in str(sq)) == 1
def aupto(limit):
  sqs = (i*i for i in range(int(limit**.5)+2) if i*i <= limit)
  return list(filter(ok, sqs))
print(aupto(131769)) # Michael S. Branicky, May 20 2021

Intersection of A000290 and A118070.

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

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A343726 Squares with exactly one even digit.

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