A033627 0-additive sequence: not the sum of any previous pair.
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
Offset: 1
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 and 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).
Programs
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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
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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[x(1+x^2+x^3)/(1-x)^2 , {x, 0, 70}], x] (* Stefano Spezia, Oct 04 2018 *) -
PARI
a(n)=if(n>2,3*n-5,n) \\ Charles R Greathouse IV, Sep 01 2016
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Python
def a(n): return 3*n-5 if n > 2 else n print([a(n) for n in range(1, 61)]) # Michael S. Branicky, Jun 09 2025
Formula
2 together with numbers of form 3k+1 (A016777).
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)
E.g.f.: 5 + 3*x + x^2/2 + exp(x)*(3*x - 5). - Stefano Spezia, Apr 15 2023
Comments