OFFSET
1,2
COMMENTS
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
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).
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)
E.g.f.: 5 + 3*x + x^2/2 + exp(x)*(3*x - 5). - Stefano Spezia, Apr 15 2023
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 *)
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved