27353 is a product of two 4k+1 primes and so it can be written as a sum of two squares in two different ways viz. 28^2+163^2 and 52^2+157^2.

27353 is a member of OEIS A025010: a(1) = 5; a(n+1) = a(n)-th non-prime, where non-primes begin at 4. The sequence can be generated as follows:

INPUT

N=[n for n in [4..100000] if is_prime(n)==0]

i=5

L=[i]

for n in range(50):

  b=N[i-1]

  L.append(b)

  i=b

print(L)

OUTPUT

[5, 10, 18, 28, 42, 60, 84, 115, 152, 198, 253, 320, 399, 494, 605, 736, 891, 1072, 1280, 1521, 1800, 2120, 2488, 2910, 3387, 3934, 4552, 5250, 6038, 6929, 7931, 9057, 10324, 11733, 13315, 15076, 17043, 19224, 21656, 24361, 27353, 30660, 34330, 38382, 42866, 47793, 53223, 59211, 65783, 73002, 80922]

27353 is a member of OEIS A041427: denominators of continued fraction convergents to sqrt(229). The sequence runs 1, 7, 8, 15, 113, 3405, 23948, 27353, 51301, 386460, ... and can be generated as follows:

INPUT

C = continued_fraction(sqrt(229))

L=[]

for i in range(1, 10):

  L.append(C.denominator(i))

print("Denominators of continued fraction are",L)

OUTPUT

Denominators of continued fraction are [7, 8, 15, 113, 3405, 23948, 27353, 51301, 386460]

27353 is a cyclic and Duffinian number.

27353 under Conway's Game of Life rules stabilises after about 680 generations into a complex mix of still lifes, oscillators (blinkers and traffic lights) and three gliders.