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Thābit ibn Qurra Number

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A Thābit ibn Qurra number, sometimes called a 321-number, is a number of the form K_n=3·2^n-1. The first few for n=0, 1, ... are 2, 5, 11, 23, 47, 95, 191, 383, 767, ... (OEIS A055010).

Note that there exist infinitely many odd integers k such that k·2^n-1 is composite for every n>=1, and numbers k with this property are called Riesel numbers.

See also

Cunningham Number, Integer Sequence Primes, Pierpont Prime, Riesel Number, Thābit ibn Qurra Prime, Thābit ibn Qurra Rule, Woodall Number

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References

Riesel, H. "Lucasian Criteria for the Primality of N=h(2^n)-1." Math. Comput. 23, 869-875, 1969.Sloane, N. J. A. Sequence and A055010 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Thābit ibn Qurra Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ThabitibnQurraNumber.html

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