A218123 Denominators of terms of the sequence {c(n)} defined in A218121.

1, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 43, 43, 43, 43, 43, 47, 47

Offset: 1

Author

Vladimir Shevelev, Oct 21 2012

Keywords

• nonn
• frac

Comments

It is easy to see that every prime is in the sequence.

Crossrefs

Cf. A218121, A217871, A217689, A217691, A217833, A217884.

Programs

Maple

ispfree := proc(a,b)
    local alow ;
    alow := floor(a);
    if nextprime(alow) < b then
        false;
    else
        true;
    end if;
end proc:
A218121c := proc(n)
    option remember;
    local k ;
    if n = 1 then
        return 1;
    elif n = 2 then
        return 5/2 ;
    else
        if ispfree(ithprime(n)/procname(n-1),ithprime(n+1)/procname(n-1)) then
            return procname(n-1) ;
        end if ;
        for k from n by -1 do
            if ispfree( ithprime(n)*ithprime(k)/ithprime(n+1),ithprime(k) )
                and ithprime(n+1)/ithprime(k) > procname(n-1) then
                return ithprime(n+1)/ithprime(k) ;
            end if;
        end do:
    end if;
end proc:
A218123 := proc(n)
    denom(A218121c(n)) ;
end proc: # R. J. Mathar, Dec 02 2012