# How Many Natural Numbers Can Get Expressed as the Sum of Consecutive Natural Numbers in only One Way? [duplicate]

Some natural numbers can be expressed as a sum of consecutive natural numbers in more than one way. For example, $7$ can get expressed both as $7$, and $(3+4).$ In terms of a sum of consecutive numbers, $4$ and $8$ can only get expressed as $4$, and $8$ respectively. Call such numbers consecutive-primes. How many consecutive-primes exist? Given all previous consecutive-primes, is there a way to compute the next consecutive-prime?

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## marked as duplicate by Ross Millikan, ShreevatsaR, Chris Eagle, t.b., Zev ChonolesMay 19 '12 at 18:32

The powers of $2$ are the only ones. The problem has been solved on this site, probably repeatedly. Here is a link. – André Nicolas May 2 '12 at 13:57