A244151 0-additive sequence: start with a(1) = 2; thereafter, a(n) = smallest number not already in sequence which is not the sum of any previous two terms.

2, 3, 4, 8, 9, 14, 15, 20, 21, 26, 27, 32, 33, 38, 39, 44, 45, 50, 51, 56, 57, 62, 63, 68, 69, 74, 75, 80, 81, 86, 87, 92, 93, 98, 99, 104, 105, 110, 111, 116, 117, 122, 123, 128, 129, 134, 135, 140, 141, 146, 147, 152, 153, 158, 159, 164, 165, 170, 171, 176, 177, 182, 183, 188, 189, 194, 195, 200, 201, 206, 207, 212, 213

Offset

1,1

Comments

As A033627, but first term is 2.

4 and the numbers in A047243. - Joerg Arndt, Jun 22 2014

Links

Table of n, a(n) for n=1..73.

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

Formula

a(2n) = 6(n-1)+2 & a(2n+1) = 6(n-1)+3 for n>1. - Robert G. Wilson v, Jun 23 2014

From Colin Barker, Jun 26 2014: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 6.

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

E.g.f.: (x^3 + 3*x^2 + 30*x + 24)/6 + (3*x - 4)*cosh(x) + 3*(x - 2)*sinh(x). - Stefano Spezia, Apr 15 2023

Mathematica

f[s_List] := Block[{k = s[[-1]] + 1, ss = Union[Plus @@@ Subsets[s, {2}]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[f, {2}, 70] (* Robert G. Wilson v, Jun 23 2014 *)

Prog

(PARI) Vec(x*(x^5+3*x^3-x^2+x+2)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Jun 26 2014

Crossrefs

Cf. A033627, A047243.

Sequence in context: A127483 A130804 A022999 * A057844 A281089 A242333

Adjacent sequences: A244148 A244149 A244150 * A244152 A244153 A244154

Keyword

nonn,easy

Author

Leonardo Sznajder, Jun 21 2014

Extensions

Added terms >= 20, Joerg Arndt, Jun 22 2014

Status

approved