

A089105


Values taken by least witness function W(n).


3



2, 3, 5, 6, 7, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26
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OFFSET

1,1


COMMENTS

19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, and 47 are in this sequence. Is this a duplicate of A007916?  Charles R Greathouse IV, Sep 07 2011
Comment from Don Reble, May 27 2014 (Start):
It has because of
 
18 565491872244422701441
20 76786041519852770748961
21 1747624437573692208710761
24 79962397898771029747829041
Alas, those are merely upperbounds on the A089825 values.
(End)
The least witness function W(k) is defined for odd composite numbers k. The sequence W(k) does not have its own entry in the OEIS because W(k) = 2 for all k with 9 <= k < 2047; then W(2047)=3.  N. J. A. Sloane, Sep 16 2014


REFERENCES

Balasubramanian, R., and S. V. Nagaraj. "The least witness of a composite number." In Information Security, LNCS 1396 (1998), pp. 6674.
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 157 (pp. 168f in the 2nd edition).


LINKS

Table of n, a(n) for n=1..20.
W. R. Alford, A. Granville, and C. Pomerance (1994). "On the difficulty of finding reliable witnesses". Lecture Notes in Computer Science 877, 1994, pp. 116.


CROSSREFS

Cf. A089825, A007916.
Sequence in context: A129125 A259444 A071591 * A028769 A094784 A085971
Adjacent sequences: A089102 A089103 A089104 * A089106 A089107 A089108


KEYWORD

nonn,hard


AUTHOR

N. J. A. Sloane, Jan 18 2004


EXTENSIONS

Missing values a(11) and a(14) added by Charles R Greathouse IV, Sep 07 2011, based on Sep 24 2010 SeqFan posting
a(13)a(20) from Charles R Greathouse IV, May 27 2014 based on comments from Charles R Greathouse IV and Don Reble


STATUS

approved



