Search: id:A086250
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%I A086250
%S A086250 0,0,0,0,0,0,0,0,0,341,2047,0,0,5461,4681,4369,0,1387,0,13981,42799,
%T A086250 15709,8388607,1105,1082401,22369621,0,645,256999,10261,0,16843009,
%U A086250 1227133513,5726623061,8727391,1729,137438953471,91625968981,647089,561
%N A086250 Smallest base-2 Fermat pseudoprime x that has ord(2,x) = n, or 0 if one 
               does not exist.
%C A086250 A base-2 Fermat pseudoprime is a composite number x such that 2^x = 2 
               mod x. For such an x, ord(2,x) is the smallest positive integer m 
               such that 2^m = 1 mod x. For a number x to have order n, it must 
               be a factor of 2^n-1 and not be a factor of 2^r-1 for r<n. Sequence 
               A086249 lists the number of pseudoprimes of order n.
%H A086250 R. G. E. Pinch, <a href="ftp://ftp.dpmms.cam.ac.uk/pub/PSP/">Pseudoprimes 
               and their factors (FTP)</a>
%H A086250 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Pseudoprime.html">Pseudoprime</a>
%e A086250 a(10) = 1 there is only 1 pseudoprime, 341 = 11*31, having order 10; 
               that is, 2^10 = 1 mod 341.
%t A086250 Table[d=Divisors[2^n-1]; num=0; i=1; done=False; While[m=d[[i]]; done=!PrimeQ[m]&&PowerMod[2, 
               m, m]==2&&MultiplicativeOrder[2, m]==n; If[done, num=m]; !done&&i<Length[d], 
               i++ ]; num, {n, 100}]
%Y A086250 Cf. A001567 (base-2 pseudoprimes), A086249.
%Y A086250 Sequence in context: A087716 A084653 A143688 this_sequence A069309 A086806 
               A006107
%Y A086250 Adjacent sequences: A086247 A086248 A086249 this_sequence A086251 A086252 
               A086253
%K A086250 hard,nonn
%O A086250 1,10
%A A086250 T. D. Noe (noe(AT)sspectra.com), Jul 14 2003

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