Definition:Fermat Number/Sequence

From ProofWiki
Jump to navigation Jump to search

Sequence of Fermat Numbers

The sequence of Fermat numbers begins:

\(\displaystyle 2^{\paren {2^0} } + 1\) \(=\) \(\displaystyle 3\)
\(\displaystyle 2^{\paren {2^1} } + 1\) \(=\) \(\displaystyle 5\)
\(\displaystyle 2^{\paren {2^2} } + 1\) \(=\) \(\displaystyle 17\)
\(\displaystyle 2^{\paren {2^3} } + 1\) \(=\) \(\displaystyle 257\)
\(\displaystyle 2^{\paren {2^4} } + 1\) \(=\) \(\displaystyle 65 \, 537\)
\(\displaystyle 2^{\paren {2^5} } + 1\) \(=\) \(\displaystyle 4 \, 294 \, 967 \, 297\)
\(\displaystyle 2^{\paren {2^6} } + 1\) \(=\) \(\displaystyle 18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 617\)

This sequence is A000215 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Sources