27307 is a member of OEIS A048573: a(n) = a(n-1) + 2*a(n-2) with a(0)=2 and a(1)=3. The sequence can be generated as follows:

INPUT

a,b=2,3

L=[a,b]

for n in [1..20]:

  c=b+2*a

  L.append(c)

  a,b=b,c

print(L)

OUTPUT

[2, 3, 7, 13, 27, 53, 107, 213, 427, 853, 1707, 3413, 6827, 13653, 27307, 54613, 109227, 218453, 436907, 873813, 1747627, 3495253]

At first I thought these number were a variant of Jacobsthal numbers but these are of the form a(n) = 2*a(n-1) + a(n-2). The generating function is (2 + x) / (1 - x - 2*x^2) and specific terms can be found using a(n) = (5*2^n + (-1)^n) / 3.

27307 is the 83rd decagonal number.

27307 is a cyclic and sphenic number.