A343726 Squares with exactly one even digit.

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

1,2

Comments

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.

Links

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

Formula

Intersection of A000290 and A118070.

Maple

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A103052 A228004 A269157 * A202303 A350835 A214937

Adjacent sequences: A343723 A343724 A343725 * A343727 A343728 A343729

Keyword

nonn,base

Author

Jon E. Schoenfield, May 19 2021

Status

approved