Positive Integer is Sum of Consecutive Positive Integers iff not Power of 2/Mistake/Second Edition

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$2$

Mistake

A positive integer is the sum of two or more consecutive integers if and only if it is not a power of $2$.

This should actually say:

A positive integer is the sum of two or more consecutive positive integers if and only if it is not a power of $2$.

It is understood that "positive integer" is taken in its strictly positive sense.

With the statement as it stands, all integers, whether positive or negative, are trivially the sum of a sequence of integers, for example:

$2 = \paren {-1} + 0 + 1 + 2$

$-4 = \paren {-4} + \paren {-3} + \paren {-2} + \paren {-1} + 0 + 1 + 2 + 3$

This mistake is in fact a partial correction to its statement in the $1986$ edition David Wells: Curious and Interesting Numbers:

An integer is the sum of a sequence of consecutive integers if and only if it is not a power of $2$.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2$