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%I #30 Jun 04 2017 09:06:54
%S 1,1,56,1,67,56,56,1,67,67,253,56,67,56,1,1,56,67,56,67,67,253,1,56,
%T 56,67,1,56,1,1,155,1,187,56,1,67,56,56,1,67,67,67,56,253,56,1,1,56,
%U 67,56,67,67,67,1,242,56,67,1,56,1,1,155,1,1,56,187,67
%N Remainder of n^340 divided by 341.
%C The n for which a(n) = 1 indicate the bases to which 341 is a Fermat pseudoprime. 341 is the smallest base 2 Fermat pseudoprime.
%C The only a(n) that occur are 0, 1, 56, 67, 155, 187, 242, 253. If n is one of these eight numbers, then a(n) = n.
%C Periodic with period 341. - _Charles R Greathouse IV_, May 01 2012
%D David Wells, Prime Numbers: The Most Mysterious Figures in Math. Hoboken, New Jersey: John Wiley & Sons (2005): 191
%H <a href="/index/Rec#order_341">Index entries for linear recurrences with constant coefficients</a>, order 341.
%e a(2) = 1 because 2^340/341 leaves a remainder of 1 (the prime factors of 2^340 - 1 include 11 and 31).
%e a(3) = 56 because 3^340/341 leaves a remainder of 56 (the prime factors of 3^340 - 56 are 5, 11, 31 and a prime number with more than a hundred digits).
%t Table[Mod[n^340, 341], {n, 100}]
%t PowerMod[Range[80],340,341] (* _Harvey P. Dale_, Jun 04 2017 *)
%o (PARI) a(n)=lift(Mod(n,341)^340) \\ _Charles R Greathouse IV_, May 01 2012
%Y Cf. A200146, A066340, A230579.
%K nonn,easy
%O 1,3
%A _Alonso del Arte_, Feb 12 2012