cp's OEIS Frontend

A033627 0-additive sequence: not the sum of any previous pair.

%I A033627 #78 Jul 22 2025 15:29:46
%S A033627 1,2,4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,52,55,58,61,64,67,
%T A033627 70,73,76,79,82,85,88,91,94,97,100,103,106,109,112,115,118,121,124,
%U A033627 127,130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175
%N A033627 0-additive sequence: not the sum of any previous pair.
%C A033627 Conjecture: a(n+1) is the number of distinct numbers of steps required for the last n digits of integers to repeat themselves by iterating the map m -> m^2 + 1. - _Ya-Ping Lu_, Oct 19 2021
%D A033627 R. K. Guy, Unsolved Problems in Number Theory, C4
%H A033627 Reinhard Zumkeller, <a href="/A033627/b033627.txt">Table of n, a(n) for n = 1..1000</a>
%H A033627 I. Dolinka, J. East and R. D. Gray, <a href="http://arxiv.org/abs/1512.02279">Motzkin monoids and partial Brauer monoids</a>, arXiv preprint arXiv:1512.02279 [math.GR], 2015 (A sequence in Table 5 appears to match this. - _N. J. A. Sloane_, Sep 17 2016)
%H A033627 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StoehrSequence.html">Stöhr Sequence</a>
%H A033627 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A033627 2 together with numbers of form 3k+1 (A016777).
%F A033627 From _Gary W. Adamson_, May 10 2008: (Start)
%F A033627 Equals binomial transform of [1, 1, 1, 0, -1, 2, -3, 4, -5, 6, -7, ...].
%F A033627 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)
%F A033627 From _Colin Barker_, Sep 19 2012: (Start)
%F A033627 a(n) = 3*n - 5, for n > 2.
%F A033627 a(n) = 2*a(n-1) - a(n-2), for n > 4;
%F A033627 G.f.: x*(1+x^2+x^3)/(1-x)^2. (End)
%F A033627 E.g.f.: 5 + 3*x + x^2/2 + exp(x)*(3*x - 5). - _Stefano Spezia_, Apr 15 2023
%t A033627 Join[{1,2},Range[4,200,3]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2012 *)
%t A033627 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 *)
%t A033627 CoefficientList[Series[x(1+x^2+x^3)/(1-x)^2 , {x, 0, 70}], x] (* _Stefano Spezia_, Oct 04 2018 *)
%o A033627 (Haskell)
%o A033627 import Data.List ((\\))
%o A033627 a033627 n = a033627_list !! (n-1)
%o A033627 a033627_list = f [1..] [] where
%o A033627    f (x:xs) ys = x : f (xs \\ (map (+ x) ys)) (x:ys)
%o A033627 -- _Reinhard Zumkeller_, Jan 11 2012
%o A033627 (PARI) a(n)=if(n>2,3*n-5,n) \\ _Charles R Greathouse IV_, Sep 01 2016
%o A033627 (Python)
%o A033627 def a(n): return 3*n-5 if n > 2 else n
%o A033627 print([a(n) for n in range(1, 61)]) # _Michael S. Branicky_, Jun 09 2025
%Y A033627 Cf. A002858, A010672, A016777.
%Y A033627 See A244151 for another version.
%K A033627 nonn,easy
%O A033627 1,2
%A A033627 _Jud McCranie_