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While experimenting, I found that every number up to 200000 except 216 is the sum of a prime and a triangular number (where 0 and 1 are included as prime). Is anything known about this?

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Why are $0$ and $1$ included as prime? They are not prime. – Michael Albanese Oct 10 '12 at 7:34
Yes: Also oeis has something – Jeremy Oct 10 '12 at 7:39
Should be reformulated as: is the sum of triagular and prime or is triangular or is triangular +1. Checking only up to 200000 and already finding one counterexample seems not very promising to me. – Hagen von Eitzen Oct 10 '12 at 7:39
Confirmed up to 10 million with the only exception being 216 (as stated by the OP) – E.O. Oct 10 '12 at 8:34

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