3 ms·

I always have a need to use this on puzzle hunts, but I don't think it ever helped.

• jacquesm 4y ago
  Quick: 2, 8, 18, 32, ?? ?
  • eesmith 4y ago
    11 distinct answers on OEIS, assuming the 2 is either the first value, or you omitted an initial 0. Which were you thinking of?
    • jacquesm 4y ago
      The 2 is the first value. And no spoilers.
      • eesmith 4y ago
        https://oeis.org/A001105 https://oeis.org/A001105 starts with 0 so I guess you don't mean that obvious quadratic. Could be https://oeis.org/A209303 https://oeis.org/A209303 : def f(n): return n*n + sum(k*k for k in map(int, str(n))) >>> [f(i) for i in range(1, 5)] [2, 8, 18, 32] but I don't know why that entry doesn't start with 0. Could be https://oeis.org/A190787 https://oeis.org/A190787 : >>> import heapq, itertools >>> seq = heapq.merge((2**i for i in itertools.count(1, 2)), (9*2**i for i in itertools.count(1, 2))) >>> list(itertools.islice(seq, 0, 4)) [2, 8, 18, 32] Or https://oeis.org/A067051 https://oeis.org/A067051: import itertools def sigma(n): return sum(i for i in range(1, n//2+1) if n % i == 0) def seq(): for n in itertools.count(1): if sigma(2*n) % 2 == 0: continue if sigma(3*n) % 3 == 0: yield n continue >>> list(itertools.islice(seq(), 0, 4)) [2, 8, 18, 32] The others are either degenerate for 4 points of the A001105 case, or are not so easy to implement in raw Python.
        • jacquesm 4y ago
          Think chemistry...
          • eesmith 4y ago
            I believe you are referring to one of the many listed ways to define https://oeis.org/A001105 https://oeis.org/A001105 , which is even more succinctly expressed as a(n) = 2*n^2. This is the answer I thought you wanted, and which I was avoiding saying. My underlying point is your sequence was under-specified, and with no clear reason to pick your preferred answer over other answers. Even knowing it's chemistry, three finite sequences which match your specification are: 2, 8, 18, 32, 18, 8, 2 2, 8, 18, 32, 21, 9, 2 2, 8, 18, 32, 32, 14, 2
  • webreac 4y ago
    50. The best answer is the simplest one. IMHO, 2n^2 is very simple.