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A033627 0-additive sequence: not the sum of any previous pair. 32
1, 2, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154, 157, 160, 163, 166, 169, 172, 175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, C4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

I. Dolinka, J. East, R. D. Gray, Motzkin monoids and partial Brauer monoids, arXiv preprint arXiv:1512.02279 [math.GR], 2015 (A sequence in Table 5 appears to match this. - N. J. A. Sloane, Sep 17 2016)

Eric Weisstein's World of Mathematics, Stöhr Sequence

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

2 together with numbers of form 3k+1.

From Gary W. Adamson, May 10 2008: (Start)

Equals binomial transform of [1, 1, 1, 0, -1, 2, -3, 4, -5, 6, -7, ...].

Equals sum of antidiagonal terms of the following arithmetic array: 1, 1, 1, 1, 1, ... 1, 2, 3, 4, 5, ... 1, 3, 5, 7, 9, ... . (End)

From Colin Barker, Sep 19 2012: (Start)

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

a(n) = 2*a(n-1) - a(n-2), for n > 4;

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

MATHEMATICA

Join[{1, 2}, Range[4, 200, 3]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

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

CoefficientList[Series[(1+x^2+x^3)/(1-x)^2 , {x, 0, 70}], x] (* Stefano Spezia, Oct 04 2018 *)

PROG

(Haskell)

import Data.List ((\\))

a033627 n = a033627_list !! (n-1)

a033627_list = f [1..] [] where

   f (x:xs) ys = x : f (xs \\ (map (+ x) ys)) (x:ys)

-- Reinhard Zumkeller, Jan 11 2012

(PARI) a(n)=if(n>2, 3*n-5, n) \\ Charles R Greathouse IV, Sep 01 2016

CROSSREFS

Cf. A002858, A010672, A016777.

See A244151 for another version.

Sequence in context: A190279 A186325 A272059 * A066512 A304116 A226596

Adjacent sequences:  A033624 A033625 A033626 * A033628 A033629 A033630

KEYWORD

nonn,easy

AUTHOR

Jud McCranie

STATUS

approved

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Last modified May 21 23:47 EDT 2019. Contains 323472 sequences. (Running on oeis4.)