# Definition:Obstinate Number

## Definition

An obstinate number is a positive odd integer which cannot be expressed as the sum of a power of $2$ and a prime.

## Sequence

The sequence of obstinate numbers begins:

$1, 127, 149, 251, 331, 337, 373, 509, 599, 701, 757, 809, 877, 905, \ldots$

## Also known as

Obstinate numbers are known according to some sources as de Polignac numbers, for Alphonse de Polignac.