Thabit number
Integer of the form 3 · 2ⁿ - 1 for non-negative n / From Wikipedia, the free encyclopedia
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In number theory, a Thabit number, Thâbit ibn Qurra number, or 321 number is an integer of the form for a non-negative integer n.
Quick Facts Named after, Conjectured no. of terms ...
Named after | Thābit ibn Qurra |
---|---|
Conjectured no. of terms | Infinite |
Subsequence of | Thabit numbers |
First terms | 2, 5, 11, 23, 47, 95, 191, 383, 6143, 786431 |
OEIS index | A007505 |
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The first few Thabit numbers are:
- 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ... (sequence A055010 in the OEIS)
The 9th century mathematician, physician, astronomer and translator Thābit ibn Qurra is credited as the first to study these numbers and their relation to amicable numbers.[1]