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## Tuesday, September 6, 2011

### Perrin numbers

Let $P(0)=3, P(1)=0, P(2)=2$ and $$P(k) = P(k-2) + P(k-3.)$$ These numbers are called the Perrin numbers. They have the interesting property that $\mod{[P(k), k]} = 0$ in almost all cases when k is prime. ( Otherwise we would have found a true prime generator! ). In any case the property holds until $k=271441.$ Interesting, isn't it? See the table below for the first 40 Perrin numbers.

 k P[k] Mod[P[k],k] PrimeQ 2 2 0 True 3 3 0 True 4 2 2 False 5 5 0 True 6 5 5 False 7 7 0 True 8 10 2 False 9 12 3 False 10 17 7 False 11 22 0 True 12 29 5 False 13 39 0 True 14 51 9 False 15 68 8 False 16 90 10 False 17 119 0 True 18 158 14 False 19 209 0 True 20 277 17 False 21 367 10 False 22 486 2 False 23 644 0 True 24 853 13 False 25 1130 5 False 26 1497 15 False 27 1983 12 False 28 2627 23 False 29 3480 0 True 30 4610 20 False 31 6107 0 True 32 8090 26 False 33 10717 25 False 34 14197 19 False 35 18807 12 False 36 24914 2 False 37 33004 0 True 38 43721 21 False 39 57918 3 False 40 76725 5 False

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Mathematics: is it the fabric of MEST?
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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)