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A077816 Wieferich numbers (1): n such that 2^A000010(n) == 1 (mod n^2). 7
1093, 3279, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, 52665, 68859, 94797, 99463, 127881, 136929, 157995, 228215, 298389, 410787, 473985, 684645, 895167, 1232361, 2053935, 2685501, 3697083, 3837523, 6161805, 11512569 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A077815(a(n)) = 1.

The only known primes are a(1)=A001220(1)=1093 and a(3)=A001220(2)=3511, the Wieferich primes.

If there are finitely many Wieferich primes (A001220), this sequence is finite. In particular, unless there are other Wieferich primes besides 1093 and 3511, this sequence consists of 104 terms with the largest being 16547533489305 (Agoh et al., 1997).

REFERENCES

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001, p. 28.

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..104 (all currently known terms)

R. Crandall, K. Dilcher, C. Pomerance, A search for Wieferich and Wilson primes, Mathematics of Computation, Volume 66, 1997.

T. Agoh, K. Dilcher, L. Skula, Fermat Quotients for Composite Moduli, Journal of Number Theory 66(1), 1997, 29-50. doi:10.1006/jnth.1997.2162

EXAMPLE

A077815(3279) = 2^A000010(3279) mod 3279^2 = 2^2184 mod 10751841 = 1, therefore 3279 is a term.

CROSSREFS

For another definition of Wieferich numbers, see A182297.

Cf. A001220.

Sequence in context: A138698 A023698 A038469 * A001220 A203858 A115192

Adjacent sequences:  A077813 A077814 A077815 * A077817 A077818 A077819

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 17 2002

EXTENSIONS

More terms from Emeric Deutsch, Mar 05 2005

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Jun 18 2005

b-file added by Max Alekseyev, Dec 18 2011

STATUS

approved

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Last modified April 16 10:39 EDT 2014. Contains 240577 sequences.