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

9, 15, 25, 27, 49, 81, 121, 125, 169, 243, 289, 343, 361, 529, 625, 729, 841, 961, 1331, 1369, 1681, 1849, 2187, 2197, 2209, 2401, 2809, 3125, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7921, 9409, 10201, 10609, 11449

Offset: 1

Author

Benoit Cloitre, Apr 09 2003

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..94

Crossrefs

Cf. A073078, A244623.

Programs

Maple

A073078 := proc(n)
    local bink,k ;
    bink := 1 ;
    for k from 1 do
        bink := 2*bink*(2-1/k) ;
        if modp(bink,n) = 0 then
            return k;
        end if;
    end do:
end proc:
A079290 := proc(n)
    option remember;
    local a;
    if n = 1 then
        9;
    else
        for a from procname(n-1)+1 do
            if not isprime(a) and 2*A073078(a) = a+1 then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Aug 20 2014

Mathematica

b[n_] := For[k=1, True, k++, If[Divisible[Binomial[2k, k], n], Return[k]]];
Select[Select[Range[12000], CompositeQ], b[#] == (# + 1)/2&] (* Jean-François Alcover, Oct 31 2019 *)

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

Extensions

a(21)-a(43) from Charles R Greathouse IV, May 24 2013