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

1,2

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.

Links

Table of n, a(n) for n=1..59.

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.

Sequence in context: A122906 A042965 A348004 * A005848 A187885 A039065

Adjacent sequences: A260000 A260001 A260002 * A260004 A260005 A260006

Keyword

nonn

Author

Natan Arie Consigli, Jul 23 2015

Status

approved