A329355 The binary expansion of a(n) is the second through n-th terms of A000002 - 1.

0, 1, 3, 6, 12, 25, 50, 101, 203, 406, 813, 1627, 3254, 6508, 13017, 26034, 52068, 104137, 208275, 416550, 833101, 1666202, 3332404, 6664809, 13329618, 26659237, 53318475, 106636950, 213273900, 426547801, 853095602, 1706191204, 3412382409, 6824764818

Offset: 1

Author

Gus Wiseman, Nov 12 2019

Keywords

• nonn

Examples

			a(11) = 813 has binary expansion q = {1, 1, 0, 0, 1, 0, 1, 1, 0, 1}, and q + 1 is {2, 2, 1, 1, 2, 1, 2, 2, 1, 2}, which is the second through 11th terms of A000002.
		

Crossrefs

Replacing "A000002 - 1" with "2 - A000002" gives A329356.

Partial sums of A000002 are A054353.

Initial subsequences of A000002 are A329360.

Cf. A211100, A275692, A288605, A296658, A329315, A329316, A329317, A329327, A329361, A329362.

Programs

Mathematica

kolagrow[q_]:=If[Length[q]<2,Take[{1,2},Length[q]+1],Append[q,Switch[{q[[Length[Split[q]]]],q[[-2]],Last[q]},{1,1,1},0,{1,1,2},1,{1,2,1},2,{1,2,2},0,{2,1,1},2,{2,1,2},2,{2,2,1},1,{2,2,2},1]]]
kol[n_Integer]:=If[n==0,{},Nest[kolagrow,{1},n-1]];
Table[FromDigits[kol[n]-1,2],{n,30}]