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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
OFFSET
0,1
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
KEYWORD
nonn
AUTHOR
Floor van Lamoen, Jun 26 2002
STATUS
approved