# Prime Sums of Squares - OEIS A360061 _Date: 2026-10-31_ ___ One day, as a shower thought while attempting to consider practical use cases of Godel-numbering-like ideas, I asked myself about sums of squares. Now, the question of `is_prime(sum([x**2 for x in range(2, n)]))` was a bit boring (sum of consecutive squares). However, for whatever reason, I thought about the case where the list of numbers to sum up came from the sequence itself. Say that the first number in the sequence is `xs[1] := 2` (1-indexed, not 0-indexed, or you could take `xs[0] := 0`). We want (pseudocode): ```python prev_sum = sum([x**2 for x in xs[:n]]) xs[n] = min(k if k > xs[n-1] and is_prime(prev_sum + k**2)) ``` Somehow, this became an OEIS sequence (2, 3, 4, 12, 48, ...): https://oeis.org/A360061 Although this completely missed the point of what I was trying to do in the first place (I think I was trying to use divisibility to represent types), I do find it funny that I have my very own OEIS entry from an arbitrary shower thought (with special thanks to a certain Peter Kagey, who is an actual mathematician).