The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A080469 Composite n such that binomial(3*n,n)==3^n (mod n). 7
 36, 57, 121, 132, 552, 8397, 7000713, 9692541, 36294723, 564033861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is prime, binomial(3*p,p)==3^p (mod p) No other terms below 10^9. A subsequence of A109641. The terms a(n) with n=2, 6, 7, 8, 9, 10 are of the form 3^k*p where p is prime and k=1, 3, 2, 5, 6, 7, respectively. It is tempting to conjecture that there are (infinitely many?) more terms of that form. - M. F. Hasler, Nov 11 2015 LINKS Table of n, a(n) for n=1..10. Max Alekseyev, PARI scripts for various problems EXAMPLE 57 is a term because binomial(3*57, 57) = 12039059761216294940321619222324879408784636200 mod 57 = 27 == 3^57 mod 57. MATHEMATICA Do[If[ !PrimeQ[n], k = Binomial[3*n, n]; m = 3^n; If[Mod[k, n] == Mod[m, n], Print[n]]], {n, 1, 70000}] (* Ryan Propper, Aug 12 2005 *) PROG (PARI) forcomposite(n=1, 1e9, binomod(3*n, n, n)==Mod(3, n)^n && print1(n", ")) \\ Cf. Alekseyev link. - M. F. Hasler, Nov 14 2015 CROSSREFS Cf. A109641, A109642; A109760, A109769. Sequence in context: A124941 A116321 A187989 * A341283 A260138 A260131 Adjacent sequences: A080466 A080467 A080468 * A080470 A080471 A080472 KEYWORD nonn,more,hard AUTHOR Benoit Cloitre, Oct 15 2003 EXTENSIONS One more term a(6) from Ryan Propper, Aug 12 2005 Four new terms a(7)-a(10) added by Max Alekseyev, Nov 05 2009 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 May 31 11:52 EDT 2023. Contains 363066 sequences. (Running on oeis4.)