A141747 - OEIS

%I #14 Feb 11 2022 07:44:28

%S 0,1,1,1,2,0,1,0,1,1,2,0,1,0,0,0,2,0,1,0,0,0,0,0,1,0,0,1,1,0,1,0,1,0,

%T 2,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,

%U 0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0

%N a(n) is the number of nonnegative integer pairs i,j such that n = 2^i + 3^j.

%H Robert Israel, <a href="/A141747/b141747.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: ( Sum_{i>=0} x^(2^i) ) * ( Sum_{j>=0} x^(3^j) ). - _Ilya Gutkovskiy_, Feb 10 2022

%e a(5) = 2, using (i,j) = (1,1) and (2,0).

%p f:= proc(n) local j,t,s;

%p   t:= 0;

%p   for j from 0 to floor(log[3](n)) do

%p     s:= n - 3^j;

%p     if s = 2^padic:-ordp(s,2) then t:= t+1 fi

%p   od;

%p   t

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Jun 08 2020

%Y Cf. A085634, A141748.

%K nonn

%O 1,5

%A _Clark Kimberling_, Jul 01 2008