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A079290 Composite numbers satisfying A073078(n)=(n+1)/2.

%I A079290 #19 Feb 04 2024 11:29:46
%S A079290 9,15,25,27,49,81,121,125,169,243,289,343,361,529,625,729,841,961,
%T A079290 1331,1369,1681,1849,2187,2197,2209,2401,2809,3125,3481,3721,4489,
%U A079290 4913,5041,5329,6241,6561,6859,6889,7921,9409,10201,10609,11449
%N A079290 Composite numbers satisfying A073078(n)=(n+1)/2.
%H A079290 Charles R Greathouse IV, <a href="/A079290/b079290.txt">Table of n, a(n) for n = 1..94</a>
%p A079290 A073078 := proc(n)
%p A079290     local bink,k ;
%p A079290     bink := 1 ;
%p A079290     for k from 1 do
%p A079290         bink := 2*bink*(2-1/k) ;
%p A079290         if modp(bink,n) = 0 then
%p A079290             return k;
%p A079290         end if;
%p A079290     end do:
%p A079290 end proc:
%p A079290 A079290 := proc(n)
%p A079290     option remember;
%p A079290     local a;
%p A079290     if n = 1 then
%p A079290         9;
%p A079290     else
%p A079290         for a from procname(n-1)+1 do
%p A079290             if not isprime(a) and 2*A073078(a) = a+1 then
%p A079290                 return a;
%p A079290             end if;
%p A079290         end do:
%p A079290     end if;
%p A079290 end proc: # _R. J. Mathar_, Aug 20 2014
%t A079290 b[n_] := For[k=1, True, k++, If[Divisible[Binomial[2k, k], n], Return[k]]];
%t A079290 Select[Select[Range[12000], CompositeQ], b[#] == (# + 1)/2&] (* _Jean-François Alcover_, Oct 31 2019 *)
%o A079290 (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 A079290 Cf. A073078, A244623.
%K A079290 nonn
%O A079290 1,1
%A A079290 _Benoit Cloitre_, Apr 09 2003
%E A079290 a(21)-a(43) from _Charles R Greathouse IV_, May 24 2013