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 A230579 a(n) = 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 L. Halbeisen and N. Hungerbühler, On generalised Carmichael numbers, Hardy-Ramanujan Society, 1999, 22 (2), pp. 8-22. (hal-01109575). See p. 8. 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) = 2*a(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

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Last modified December 3 11:13 EST 2021. Contains 349462 sequences. (Running on oeis4.)