

A244749


0additive sequence: a(n) is the smallest number larger than a(n1) that is not the sum of any subset of earlier terms, starting with initial values {2, 5}.


1



2, 5, 6, 9, 10, 28, 29, 85, 86, 256, 257, 769, 770, 2308, 2309, 6925, 6926, 20776, 20777, 62329, 62330, 186988, 186989, 560965, 560966, 1682896, 1682897, 5048689, 5048690, 15146068, 15146069, 45438205, 45438206, 136314616, 136314617, 408943849, 408943850, 1226831548, 1226831549
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OFFSET

1,1


COMMENTS

This sequence differs from A003664.


REFERENCES

R. K. Guy, "sAdditive sequences," preprint, 1994.


LINKS

Table of n, a(n) for n=1..39.
S. R. Finch, Are 0additive sequences always regular?, Amer. Math. Monthly, 99 (1992), 671673.
Index entries for linear recurrences with constant coefficients, signature (1,3,3).


FORMULA

a(2n) = 4a(2n  2)  3a(2n  4) and a(2n +1) = a(2n) +1, for n>2.
a(n) = a(n1) + 3*a(n2) + 3*a(n3) for n>6.  Colin Barker, Jul 11 2014
G.f.: x*(7*x^5+14*x^4+6*x^35*x^27*x2) / ((x+1)*(3*x^21)).  Colin Barker, Jul 11 2014


EXAMPLE

The numbers 1127 are not in the sequence since some combination of the previous terms add to it. example 17=2+5+10.
The number 28 however is a term since no combination of the previous terms cannot be found which sum to 28.


MATHEMATICA

f[s_List] := f[n] = Block[{k = s[[1]] + 1, ss = Union[ Plus @@@ Subsets[s]]}, While[ MemberQ[ss, k], k++]; Append[s, k]]; Nest[ f[#] &, {2, 5}, 20] (* or *)
b = LinearRecurrence[{4, 3}, {9, 28}, 18]; Join[{2, 5, 6}, Riffle[b, b + 1]]
Join[{2, 5, 6}, LinearRecurrence[{1, 3, 3}, {9, 10, 28}, 36]] (* Ray Chandler, Aug 03 2015 *)


PROG

(PARI) Vec(x*(7*x^5+14*x^4+6*x^35*x^27*x2)/((x+1)*(3*x^21)) + O(x^100)) \\ Colin Barker, Jul 11 2014


CROSSREFS

Cf. A003662, A003663, A005408, A026471, A026474, A033627, A051039, A051040, A244151, A244750.
Cf. A060469  A060472.
Sequence in context: A309242 A122701 A032925 * A166087 A281902 A153143
Adjacent sequences: A244746 A244747 A244748 * A244750 A244751 A244752


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane and Robert G. Wilson v, Jul 05 2014


STATUS

approved



