The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209833 a(f(A074773(n))) = A074773(n); 1 <= n <= 9999; f: N -> {1..9999}. 3
 457453568161, 1362242655901, 2152302898747, 2273312197621, 4341937413061, 4777422165601, 11377272352951, 13112583010129, 23537786498641, 90022554326251, 92045875072861, 131175316104661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also a table "a" of the 9999 smallest strong pseudoprimes to bases 2,3,5, and 7, indexed by function f. See the expression of f in the first PARI program. The algorithm below is a fast deterministic primality test for integers x, x <= A074773(10000)-1. Note that A074773(10000)-1 > 5.6*10^18 > 2^62. 1. Run Rabin-Miller test only with base 2. If x not pass return composite. 2. Run Rabin-Miller test only with base 3. If x not pass return composite. 3. Run Rabin-Miller test only with base 5. If x not pass return composite. 4. Run Rabin-Miller test only with base 7. If x not pass return composite. 5. Compute i = f(x); if a(i) = x, return composite; otherwise return prime. --- In first reference, p. 1022, there is a test where a table of strong pseudoprimes is used. Terms computed using data from Charles R Greathouse IV. See A074773. Third link references file "C:/temp/A.txt", a string with the first 9999 terms of A074773, each term preceded by its number of digits. Second link references file "C:/temp/V.txt", which makes the table V used by function f. It is also a string of numbers, each one preceded by its number of digits. LINKS Table of n, a(n) for n=1..12. Washington Bomfim, C:/temp/V.txt Washington Bomfim, C:/temp/A.txt C. Pomerance, J. L. Selfridge, and S. S. Wagstaff, Jr., The pseudoprimes to 25*10^9, Mathematics of Computation 35 (1980), pp. 1003-1026. Eric Weisstein's World of Mathematics, Rabin-Miller Strong Pseudoprime Test EXAMPLE a(1) = A074773(6) because f(A074773(6)) = 1. (With M = 16992, A074773(6) % 453359393 % M + 1 = 7185, and A074773(6)%450577199 % M + 1 = 7593. After running the first PARI program, one can type V[7185], and V[7593] to see that y=z = V[7185]= V[7593] = 0. So f(A074773(6)) = 1). PROG (PARI) s=Str(read("C:/temp/V.txt")); x=Vec(s); n=0; M=16992; i=1; V=vector(M); k=0; s=""; j=0; y=0; z=0; for(n=1, M, k=i+1; s=""; for(j=1, eval(x[i]), s=concat(s, x[k]); k++); V[n]=eval(s); i=k); \\ f(x)={y=V[x%453359393%M+1]; z=V[x%450577199%M+1]; return((y<=z)*z + (y>z)*y +1); }; \\ print("Reading file C:/temp/A.txt. Please wait..."); s=Str(read("C:/temp/A.txt")); x=Vec(s); i=1; p=vector(9999); for(n=1, 9999, k=i+2; s=""; for(j=1, eval(concat(x[i], x[i+1])), s=concat(s, x[k]); k++); p[n]=eval(s); i=k); print(""); a=vector(9999); for(i=1, 9999, a[f(p[i])]=p[i]); for(i=1, 9999, print(i, " ", a[i])) CROSSREFS Cf. A208846. Sequence in context: A218865 A289111 A364785 * A255578 A239921 A250867 Adjacent sequences: A209830 A209831 A209832 * A209834 A209835 A209836 KEYWORD nonn,fini,full AUTHOR Washington Bomfim, Mar 14 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)