Definition:Obstinate Number

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


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