A079290 - OEIS

%I #19 Feb 04 2024 11:29:46

%S 9,15,25,27,49,81,121,125,169,243,289,343,361,529,625,729,841,961,

%T 1331,1369,1681,1849,2187,2197,2209,2401,2809,3125,3481,3721,4489,

%U 4913,5041,5329,6241,6561,6859,6889,7921,9409,10201,10609,11449

%N Composite numbers satisfying A073078(n)=(n+1)/2.

%H Charles R Greathouse IV, <a href="/A079290/b079290.txt">Table of n, a(n) for n = 1..94</a>

%p A073078 := proc(n)

%p     local bink,k ;

%p     bink := 1 ;

%p     for k from 1 do

%p         bink := 2*bink*(2-1/k) ;

%p         if modp(bink,n) = 0 then

%p             return k;

%p         end if;

%p     end do:

%p end proc:

%p A079290 := proc(n)

%p     option remember;

%p     local a;

%p     if n = 1 then

%p         9;

%p     else

%p         for a from procname(n-1)+1 do

%p             if not isprime(a) and 2*A073078(a) = a+1 then

%p                 return a;

%p             end if;

%p         end do:

%p     end if;

%p end proc: # _R. J. Mathar_, Aug 20 2014

%t b[n_] := For[k=1, True, k++, If[Divisible[Binomial[2k, k], n], Return[k]]];

%t Select[Select[Range[12000], CompositeQ], b[#] == (# + 1)/2&] (* _Jean-François Alcover_, Oct 31 2019 *)

%o (PARI) p=5;forprime(q=7,1e4,forstep(n=p+2,q-2,2, for(s=2,n\2, if(binomial(2*s,s)%n==0,next(2)));print1(n", ")); p=q) \\ _Charles R Greathouse IV_, May 24 2013

%Y Cf. A073078, A244623.

%K nonn

%O 1,1

%A _Benoit Cloitre_, Apr 09 2003

%E a(21)-a(43) from _Charles R Greathouse IV_, May 24 2013