cp's OEIS Frontend

A260003 Values f(1,x,y) with x>=0, y>0, in increasing order, where f is the Sudan function defined in A260002.

%I A260003 #34 Jan 11 2020 15:57:47
%S A260003 1,3,4,5,7,8,9,11,12,13,15,16,17,19,20,21,24,25,26,27,28,29,31,32,33,
%T A260003 35,36,37,39,40,41,42,43,44,45,47,48,49,51,52,53,55,56,57,58,59,60,61,
%U A260003 63,64,65,66,67,69,71,72,73,74,75
%N A260003 Values f(1,x,y) with x>=0, y>0, in increasing order, where f is the Sudan function defined in A260002.
%C A260003 Equivalently, numbers of the form 2^y(x+2)-y-2.
%C A260003 Using f(1,x,y) = f(0, f(1,x,y-1), f(1,x,y-1)+y) = 2*f(1,x,y-1) + y
%C A260003 f(1,x,y) + y + 2 = 2*(f(1,x,y-1)+y-1+2) let g(y) = f(1,x,y) + y + 2 then g(y) = 2*g(y-1). This means g(y)=2^y*g(0) and f(1,x,y) + y + 2 = 2^y(f(1,x,0)+2) but f(1,x,0) = x so f(1,x,y) = 2^y(x+2) - y - 2.
%C A260003 In this list we suppose that y>0. If we include y=0, every natural number would be in the sequence.
%e A260003 19 is listed because f(1,1,3) = 2^3*(1+2) - 3 - 2 = 19.
%Y A260003 Cf. A000325 (f(1,2,n)), A005408 (f(1,n,1)=2n+1), A048493 (f(1,n,2)), A079583 (f(1,1,n)), A123720 (f(1,4,n)), A133124(f(1,3,n)), A260002, A260004, A260005 (f(2,n,2)), A260006.
%K A260003 nonn
%O A260003 1,2
%A A260003 _Natan Arie Consigli_, Jul 23 2015