A062547 a(n) is least odd integer not a partial sum of 1, 3, ..., a(n-1).

1, 3, 5, 7, 17, 19, 53, 55, 161, 163, 485, 487, 1457, 1459, 4373, 4375, 13121, 13123, 39365, 39367, 118097, 118099, 354293, 354295, 1062881, 1062883, 3188645, 3188647, 9565937, 9565939, 28697813, 28697815, 86093441, 86093443, 258280325, 258280327, 774840977

Offset: 0

Author

Wouter Meeussen, Jun 26 2001

Keywords

• nonn
• easy

Examples

			Partial sums of 1;3;5 are 1;3;4;5;6;8;9 and 7 is the least missing odd integer, hence the next term is 7.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,3,3).

Crossrefs

Cf. A048473, A052919, A062548.

Programs

Mathematica

Table[ -1+ 2 3^Floor[k/2]+2 Mod[k, 2], {k, 0, 36}]
LinearRecurrence[{-1,3,3},{1,3,5},40] (* Harvey P. Dale, Jul 14 2018 *)

Formula

a(2*n) = A048473(n); a(2n+1) = a(2n)+2.

For n > 0, a(2*n) = 3*a(2*n-1) - 4; a(2*n+1) = a(2*n) + 2 = A052919(n+1).

From Bruno Berselli, Jan 28 2011: (Start)

G.f.: (1+4*x+5*x^2)/((1+x)*(1-3*x^2)).

a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) for n > 2.

a(n) = 2*3^((2*n + (-1)^n - 1)/4) - (-1)^n. (End)

Extensions

Edited by Michel Marcus, Mar 16 2024