A282432 Number of primes of the form n - 3^k.

0, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 0, 1, 0, 3, 0, 2, 0, 1, 0, 2, 0, 1, 1, 2, 0, 4, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 3, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 1, 2, 0, 3, 0, 3, 0, 1, 0, 3, 0, 2, 0, 0, 0, 4, 0, 3, 0, 1, 0, 3, 0

Offset: 1

Author

Arkadiusz Wesolowski, Feb 15 2017

Keywords

• nonn
• easy

Examples

			a(14) = 3; 14 - 3^0 = 13, 14 - 3 = 11, 14 - 3^2 = 5, three primes.
		

Crossrefs

Cf. A109925, A282430.

Programs

Magma

lst:=[]; for n in [1..105] do c:=0; e:=Floor(Log(3, n)); k:=0; while k le e do p:=n-3^k; if IsPrime(p) then c+:=1; end if; k+:=1; end while; Append(~lst, c); end for; lst;

Maple

A282432 := proc(n)
    a := 0 ;
    for k from 0 do
        if n-3^k < 2 then
            return a ;
        elif isprime(n-3^k) then
            a := a+1 ;
        end if;
    end do:
end proc:
seq(A282432(n),n=1..80) ; # R. J. Mathar, Mar 07 2022

PARI

ispp3(n) = (n==1) || (n==3) || (ispower(n,,&p) && (p==3));
a(n) = {my(nb = 0); forprime(p=2, n, nb += ispp3(n-p);); nb;} \\ Michel Marcus, Feb 18 2017

Formula

a(A282430(n)) = 0.

G.f.: ( Sum_{i>=0} x^(3^i) ) * ( Sum_{j>=1} x^prime(j) ). - Ilya Gutkovskiy, Feb 10 2022