

A260003


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


4



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
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OFFSET

1,2


COMMENTS

Equivalently, numbers of the form 2^y(x+2)y2.
Using f(1,x,y) = f(0, f(1,x,y1), f(1,x,y1)+y) = 2*f(1,x,y1) + y
f(1,x,y) + y + 2 = 2*(f(1,x,y1)+y1+2) let g(y) = f(1,x,y) + y + 2 then g(y) = 2*g(y1). 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.


LINKS



EXAMPLE

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.


KEYWORD

nonn


AUTHOR



STATUS

approved



