A085999 - OEIS

%I #10 Mar 27 2021 08:00:11

%S 561,645,1729,341,1105,561,1387,2047,2465,341,2701,6601,645,4371,8321,

%T 13747,29341,8911,19951,1387,30889,88561,2047,18721,60701,31621,

%U 680627,4033,3277,1905,357761,74665,1419607,88357,4681,8321,422659,83333

%N For p = prime(n), a(n) is the smallest base-2 pseudoprime N (that is, 2^(N-1) = 1 mod N) such that p divides N.

%C Tables compiled by Pinch were used. Sequence A086000 lists a(n) / prime(n).

%H Amiram Eldar, <a href="/A085999/b085999.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(11) = 341 because prime(11) = 31 and 341 is the first pseudoprime divisible by 31.

%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++ ]; psp, {n, 2, 100}]

%Y Cf. A001567 (base-2 pseudoprimes), A086000.

%K easy,nonn

%O 2,1

%A _T. D. Noe_, Jul 08 2003