27538 is a product of 2, a 4k+3 prime raised to an even power and a 4k+1 prime. It can therefore be expressed as a sum of two squares in one way only viz. 147^2 + 77^2.

27538 is a member of OEIS A093472: (2n+1)-digit numbers whose first and last digits add to ten, second and next-to-last add to ten and so on with the central digit a 5.

The sequence can be generated using the following code:

INPUT

L=[]

OK=0

target=5

for n in [100..99999]:

  D=n.digits()

  if len(D)%2==1:

    if D[(len(D)-1)/2]==target:

      OK=1

      for i in range((len(D)-1)/2):

        if D[i]+D[len(D)-i-1] != target*2:

          OK=0

          break

      if OK==1:

        L.append(n)

print(L)

OUTPUT

[159, 258, 357, 456, 555, 654, 753, 852, 951, 11599, 12589, 13579, 14569, 15559, 16549, 17539, 18529, 19519, 21598, 22588, 23578, 24568, 25558, 26548, 27538, 28528, 29518, 31597, 32587, 33577, 34567, 35557, 36547, 37537, 38527, 39517, 41596, 42586, 43576, 44566, 45556, 46546, 47536, 48526, 49516, 51595, 52585, 53575, 54565, 55555, 56545, 57535, 58525, 59515, 61594, 62584, 63574, 64564, 65554, 66544, 67534, 68524, 69514, 71593, 72583, 73573, 74563, 75553, 76543, 77533, 78523, 79513, 81592, 82582, 83572, 84562, 85552, 86542, 87532, 88522, 89512, 91591, 92581, 93571, 94561, 95551, 96541, 97531, 98521, 99511]

Compare this number property with similar number properties discussed in blog posts titled:

• Balanced Numbers (24th March 2023)
• Digitally Balanced Numbers (31st March 2023)
• More About Balanced Numbers (3rd March 2024)

Not related but bearing the descriptor "balanced" are the balanced primes discussed in a blog post titled Varieties of Balanced Primes on 16th May 2017.

27538 has a circulant matrix with a determinant that is a cubic number viz. 125 = 5^3.

27538 cannot be rendered as a digit equation:

*NO_EQUATION*