1,1

Composites that pass the Miller-Rabin test for bases 2 and 3. The intersection of A001262 (strong pseudoprimes to base 2) and A020229 (strong pseudoprimes to base 3).

The Washington Bomfim link references a table with all terms up to 2^64. Data from Jan Feitsma and William Galway, see link below, permitted an easy determination of these terms. I tested the Mathematica function PrimeQ[n] with those numbers to verify that it is correct for all n < 2^64. - Washington Bomfim, May 13 2012

Don Reble, Table of n, a(n) for n = 1..10000

Joerg Arndt, Matters Computational (The Fxtbook), section 39.10, pp. 786-792

D. Bleichenbacher, Thesis and strong pseudoprimes to 2 and 3 up to 10^16

Washington Bomfim, Table of n, a(n) for n=1..1499371 [a large file]

Jan Feitsma and William Galway, Tables of pseudoprimes and related data

A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography, section 4.2.3, Miller-Rabin test.

Eric Weisstein's World of Mathematics, Rabin-Miller test

Index entries for sequences related to pseudoprimes

nmax = 10^8; sppQ[n_?EvenQ, _] := False; sppQ[n_?PrimeQ, _] := False; sppQ[n_, b_] := (s = IntegerExponent[n - 1, 2]; d = (n - 1)/2^s; If[ PowerMod[b, d, n] == 1, Return[True], Do[ If[ PowerMod[b, d*2^r, n] == n-1, Return[True]], {r, 0, s-1}]]); A072276 = {}; n = 1; While[n < nmax, n = n+2; If[sppQ[n, 2] && sppQ[n, 3] , Print[n]; AppendTo[ A072276, n]]]; A072276 (* Jean-François Alcover, Oct 20 2011, after R. J. Mathar *)

Cf. A001262, A006945, A014233, A020229.

Sequence in context: A191820 A074999 A347279 * A114657 A250058 A205205

Adjacent sequences: A072273 A072274 A072275 * A072277 A072278 A072279

nonn

Francois R. Grieu, Jul 09 2002

approved