A039739 a(n)=2*q-prime(n), where q is the prime < p(n) for which (prime(n) mod q) is maximal.

1, 1, 3, 3, 1, 5, 3, 3, 5, 3, 1, 5, 3, 11, 5, 3, 1, 7, 3, 1, 3, 3, 5, 9, 5, 3, 11, 9, 5, 7, 3, 5, 3, 9, 7, 1, 3, 11, 5, 15, 13, 3, 1, 5, 3, 3, 3, 27, 25, 21, 15, 13, 3, 5, 11, 5, 3, 1, 17, 15, 5, 7, 3, 1, 9, 3, 9, 11, 9, 5, 3, 15, 9, 3, 3, 5, 1, 21, 13, 3, 1

Offset: 2

Author

Clark Kimberling

Keywords

• nonn

Programs

Maple

A039739 := proc(n)
    local p,maxmod,q,qpiv ;
    p := ithprime(n) ;
    for j from 1 to n-1 do
        q := ithprime(j) ;
        if j = 1 then
            qpiv := q ;
            maxmod := modp(p,q) ;
        else
            if modp(p,q) > maxmod then
                maxmod := modp(p,q) ;
                qpiv := q ;
            end if;
        end if;
    end do:
    2*qpiv-p ;
end proc:
seq(A039739(n),n=2..80) ; # R. J. Mathar, May 03 2021

Formula

a(n) = 2*A039734(n)-prime(n). - R. J. Mathar, May 03 2021