A123317 Smallest prime power m such that n+m is a prime number.

1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 8, 5, 4, 3, 2, 1, 2, 1, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 32, 5, 4, 3, 2, 1, 8, 5, 4, 3, 2, 1, 2, 1, 256, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 128, 5, 4, 3, 2, 1, 8, 7, 16, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1

Offset

1,3

Links

Table of n, a(n) for n=1..102.

Formula

A123318(n) = n + a(n);

a(A006093(n)) = 1; a(A040976(n)) = 2 for n>2.

Example

n=23: 23+1=3*2^3, 23+2=5^2, 23+3=13*2, 23+2^2=3^3, 23+5=7*2^2, 23+7=5*3*2, but 23+8=31=A000040(11), therefore a(23)=8;
n=24: 24+1=5^2, 24+2=13*2, 24+3=3^3, 24+2^2=7*2^2, but 24+5=29=A000040(10), therefore a(24)=5;
the smallest occurring proper odd prime power is 9=3^2:
n=118: 118+1=17*7, 118+2=5*3*2^3, 118+3=11^2, 118+2^2=61*2, 118+5=41*3, 118+7=5^3, 118+2^3=7*2*3^2, but 118+3^2=127=A000040(31), therefore a(118)=9.

Maple

A123317 := proc(n)
    local m ;
    m :=1 ;
    if isprime(n+m) then
        return m ;
    end if;
    for m from 2 do
        if nops(numtheory[factorset](m)) = 1 then
            if isprime(n+m) then
                return m;
            end if;
        end if;
    end do:
end proc:
seq(A123317(n), n=1..102) ; # R. J. Mathar, Aug 09 2019

Crossrefs

Cf. A013632, A000961.

Sequence in context: A352933 A276976 A135545 * A231557 A171453 A285707

Adjacent sequences: A123314 A123315 A123316 * A123318 A123319 A123320

Keyword

nonn

Author

Reinhard Zumkeller, Sep 27 2006

Status

approved