Definition:Fermat Number/Sequence
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Sequence of Fermat Numbers
The sequence of Fermat numbers begins:
| \(\ds 2^{\paren {2^0} } + 1\) | \(=\) | \(\ds 3\) | ||||||||||||
| \(\ds 2^{\paren {2^1} } + 1\) | \(=\) | \(\ds 5\) | ||||||||||||
| \(\ds 2^{\paren {2^2} } + 1\) | \(=\) | \(\ds 17\) | ||||||||||||
| \(\ds 2^{\paren {2^3} } + 1\) | \(=\) | \(\ds 257\) | ||||||||||||
| \(\ds 2^{\paren {2^4} } + 1\) | \(=\) | \(\ds 65 \, 537\) | ||||||||||||
| \(\ds 2^{\paren {2^5} } + 1\) | \(=\) | \(\ds 4 \, 294 \, 967 \, 297\) | ||||||||||||
| \(\ds 2^{\paren {2^6} } + 1\) | \(=\) | \(\ds 18 \, 446 \, 744 \, 073 \, 709 \, 551 \, 617\) |
This sequence is A000215 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Fermat number (P. de Fermat, 1640)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Fermat number (P. de Fermat, 1640)