login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A230579 2^n mod 341. 1
1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171, 1, 2, 4, 8, 16, 32, 64, 128, 256, 171 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Jeans asserts that it would have been impossible for the ancient Chinese to have discovered a case of failure for the converse of Fermat's little theorem because the smallest counterexample "(n = 341) consists of 103 figures" in base 10.

Granted that without a computer, the task of calculating 2^340 - 1 and dividing by 341 is tedious and error-prone, thus discouraging the discovery of that number as a counterexample to the so-called Chinese hypothesis.

But by instead computing just a few dozen powers of 2 modulo 341, it becomes readily apparent that the sequence of powers of 2 modulo 341 has a period of length 10 and therefore 2^340 = 1 mod 341, yet 341 = 11 * 31, which is not a prime number.

LINKS

Table of n, a(n) for n=0..69.

J. H. Jeans, The converse of Fermat's theorem, Messenger of Mathematics 27 (1898), p. 174.

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1,-1,1).

FORMULA

a(0) = 1, a(n) = 2a(n - 1) mod 341.

EXAMPLE

a(8) = 256 because 2^8 = 256.

a(9) = 171 because 2^9 = 512 and 512 - 341 = 171.

a(10) = 1 because 2 * 171 = 342 and 342 - 341 = 1.

MATHEMATICA

PowerMod[2, Range[0, 79], 341]

LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1}, {1, 2, 4, 8, 16, 32, 64, 128, 256}, 70] (* Ray Chandler, Jul 12 2015 *)

PROG

(PARI) a(n)=lift(Mod(2, 341)^n) \\ Charles R Greathouse IV, Mar 22 2016

CROSSREFS

Cf. A206786.

Sequence in context: A243086 A087079 A252757 * A009694 A275816 A097000

Adjacent sequences:  A230576 A230577 A230578 * A230580 A230581 A230582

KEYWORD

nonn,easy

AUTHOR

Alonso del Arte, Oct 23 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 4 21:14 EST 2020. Contains 338938 sequences. (Running on oeis4.)