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

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, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 71, 72, 73, 74, 75

Offset: 1

Author

Natan Arie Consigli, Jul 23 2015

Keywords

• nonn

Comments

Equivalently, numbers of the form 2^y(x+2)-y-2.

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

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.

In this list we suppose that y>0. If we include y=0, every natural number would be in the sequence.

Examples

			19 is listed because f(1,1,3) = 2^3*(1+2) - 3 - 2 = 19.
		

Crossrefs

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.