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A072134 Second generation sequence in which each number is skipped that can be written as sum of distinct previous entries. To make the first generation we start with all natural numbers: this gives the powers of 2 (A000079). For the second generation we start with the natural numbers from which are removed the numbers of the first generation. 0
3, 5, 6, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..34.

FORMULA

a_n is the union of {3, 6}; the numbers {v_n} where v_0 = 5, v_n=3*v_{n-1}+2; and the numbers u_n = 2 + v_n.

Conjectures from Colin Barker, Sep 09 2017: (Start)

G.f.: (3 + 8*x + 2*x^2 - 11*x^3 - 9*x^4 - 3*x^5) / ((1 + x)*(1 - 3*x^2)).

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

a(n) = -a(n-1) + 3*a(n-2) + 3*a(n-3) for n>5.

(End)

EXAMPLE

4 is not in the sequence because it is in A000079.

14 is not in the sequence because 14 = 3+5+6.

CROSSREFS

Sequence in context: A163620 A227722 A250419 * A179220 A290577 A145736

Adjacent sequences:  A072131 A072132 A072133 * A072135 A072136 A072137

KEYWORD

nonn

AUTHOR

Floor van Lamoen, Jun 26 2002

STATUS

approved

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Last modified June 19 12:57 EDT 2019. Contains 324222 sequences. (Running on oeis4.)