# Definition:Obstinate Number

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## 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:

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

This sequence is A006285 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

## Also known as

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

## Also see

- De Polignac's False Conjecture
- Results about
**obstinate numbers**can be found here.