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 A007538 A self-generating sequence: there are a(n) 3's between successive 2's. (Formerly M0432) 13
 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS (a(n)) is the unique fixed point of the morphism 2->233, 3->2333 (immediate from its definition). - Michel Dekking, Feb 21 2017 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 Bryce Emerson Blackham, Subtraction Games: Range and Strict Periodicity, Master's thesis, 2018. The Fifty-Fourth William Lowell Putnam Mathematical Competition, Problem A-6, Amer. Math. Monthly, 101 (1994), 727-728. The Fifty-Fourth William Lowell Putnam Mathematical Competition, Problem A-6, Math. Mag., 67 (No. 2, 1994), 157-158. FORMULA a(n) = floor( n*(1+sqrt(3)) ) - floor( (n-1)*(1+sqrt(3)) ). a(n) = f(n,2,2,2) with f(n,b,c,i) = if n=1 then b else (if c=0 then f(n-1,2,a(i),i+1) else f(n-1,3,c-1,i)). [Reinhard Zumkeller, May 25 2009] a(n) = A080757(n-1) + 1; a(n) = A188068(n) + 2. [Reinhard Zumkeller, Feb 14 2012] a(A188069(n)) = 2; a(A188070(n)) = 3. - Reinhard Zumkeller, Feb 14 2012 MATHEMATICA f[n_, b_, c_, i_] := f[n, b, c, i] = If[n == 1, b, If[c == 0 , f[n-1, 2, a[i], i+1], f[n-1, 3, c-1, i]]]; a[n_] := f[n, 2, 2, 2]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 15 2013, after Reinhard Zumkeller *) Table[Floor[n (1 + Sqrt@ 3)] - Floor[(n - 1) (1 + Sqrt@ 3)], {n, 120}] (* Michael De Vlieger, Oct 08 2016 *) PROG (Haskell) a007538 n = f n 2 2 2 where    f 1 b _ _ = b    f n b 0 i = f (n - 1) 2 (a007538 i) (i + 1)    f n b c i = f (n - 1) 3 (c - 1) i -- Reinhard Zumkeller, Feb 14 2012 CROSSREFS Sequence in context: A102313 A262955 A276859 * A242285 A238756 A025076 Adjacent sequences:  A007535 A007536 A007537 * A007539 A007540 A007541 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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Last modified June 25 08:27 EDT 2021. Contains 345453 sequences. (Running on oeis4.)