login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

N. J. A. Sloane, Simon Plouffe

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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