While experimenting, I found that every number up to $200000$, with the sole exception of $216$ 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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4Why are $0$ and $1$ included as prime? They are not prime. – Michael Albanese Oct 10 '12 at 07:34
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5Yes: http://arxiv.org/abs/0803.3737 Also oeis has something – Jemmy Oct 10 '12 at 07:39
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2Should 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 07:39
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3Confirmed up to 10 million with the only exception being 216 (as stated by the OP) – E.O. Oct 10 '12 at 08:34
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@E.O. Did you happen to check up to higher numbers? – Ovi Nov 26 '16 at 08:05