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

1,2

Comments

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

Links

Table of n, a(n) for n=1..80.

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

Crossrefs

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

Sequence in context: A029084 A032229 A024366 * A288157 A333701 A140682

Adjacent sequences: A218120 A218121 A218122 * A218124 A218125 A218126

Keyword

nonn,frac

Author

Vladimir Shevelev, Oct 21 2012

Status

approved