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%I #11 Mar 27 2021 08:00:15
%S 187,129,247,31,85,33,73,89,85,11,73,161,15,93,157,233,481,133,281,19,
%T 391,1067,23,193,601,307,6361,37,29,15,2731,545,10213,593,31,53,2593,
%U 499,1205,141155,1261,2281,97,3333,1387,1891,1777,3391,381,59,20231,97
%N For p = prime(n), a(n) is the smallest N such that pN is a base-2 pseudoprime (that is, 2^(pN-1) = 1 mod pN).
%C Tables compiled by Pinch were used. Sequence A085999 lists a(n)*prime(n). It can be shown that a(n) has the form 1 + 2 ord(4, prime(n)) k for some k > 0, where the ord(x,y) function is the smallest positive integer r such that x^r = 1 mod y. The value of k for a(n) is given in sequence A086001. Note that prime(n) divides 2^a(n) - 2. Compare A085012, which gives the smallest prime q such that pq is a 2-pseudoprime.
%H Amiram Eldar, <a href="/A086000/b086000.txt">Table of n, a(n) for n = 2..10001</a>
%H R. G. E. Pinch, <a href="ftp://ftp.dpmms.cam.ac.uk/pub/PSP/">Pseudoprimes and their factors (FTP)</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pseudoprime.html">Pseudoprime</a>.
%e a(2) = 187 because prime(2) = 3 and N=187 is the smallest number such that 3N is a 2-pseudoprime.
%t Table[p=Prime[n]; m=MultiplicativeOrder[4, p]; k=1; While[psp=p(1+2*m*k); PowerMod[2, psp-1, psp]!=1, k++ ]; 1+2*m*k, {n, 2, 100}]
%Y Cf. A001567 (base-2 pseudoprimes), A082654 (ord(4, p)), A085012, A085999, A086001.
%K easy,nonn
%O 2,1
%A _T. D. Noe_, Jul 08 2003