

A061107


a(0) = 0, a(1) = 1, a(n) is the concatenation of a(n2) and a(n1) for n > 1.


6




OFFSET

0,3


COMMENTS

Original name was: In the Fibonacci rabbit problem we start with an immature pair 'I' which matures after one season to 'M'. This mature pair after one season stays alive and breeds a new immature pair and we get the following sequence I, MI, MIM, MIMMI, MIMMIMIM, MIMMIMIMMIMMI... if we replace 'I' by a '0' and 'M' by a '1' we get the required binary sequence.


REFERENCES

Amarnath Murthy, Smarandache Reverse auto correlated sequences and some Fibonacci derived sequences, Smarandache Notions Journal Vol. 12, No. 123, Spring 2001.
Ian Stewart, The Magical Maze.


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..15


FORMULA

a(0) = 0, a(1) =1, a(n) = concatenation of a(n1) and a(n2).
a(n) = a(n1)*2^floor(log_2(a(n2))+1)+a(n2), for n>2, a(2)=10 (base 2).  Hieronymus Fischer, Jun 26 2007
a(n) = A036299(n1), n>0.  R. J. Mathar, Oct 02 2008
a(n) can be transformed by a(n1) when you change every single "1"(from a(n1)) into "10" and every single "0"(from a(n1)) into "1". [YuJiping and Sirius Caffrey, Apr 30 2015]


EXAMPLE

a(0) = 0, a(1) = 1, a(2) = a(1)a(0)= 10, etc.


MAPLE

A[0]:= 0: A[1]:= 1: A[2]:= 10:
for n from 3 to 20 do
A[n]:= 10^(ilog10(A[n2])+1)*A[n1]+A[n2]
od:
seq(A[n], n=0..10); # Robert Israel, Apr 30 2015


MATHEMATICA

nxt[{a_, b_}]:={b, FromDigits[Join[IntegerDigits[b], IntegerDigits[a]]]}; Transpose[NestList[nxt, {0, 1}, 10]][[1]] (* Harvey P. Dale, Jul 05 2015 *)


PROG

(PARI) { default(realprecision, 100); L=log(10); for (n=0, 15, if (n>2, a=a1*10^(log(a2)\L + 1) + a2; a2=a1; a1=a, if (n==0, a=0, if (n==1, a=a2=1, a=a1=10))); write("b061107.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 18 2009


CROSSREFS

Cf. A063896, A131242. See A005203 for the sequence version converted to decimal.
Column k=10 of A144287.
Sequence in context: A162849 A041182 A036299 * A015498 A266283 A039393
Adjacent sequences: A061104 A061105 A061106 * A061108 A061109 A061110


KEYWORD

base,nonn,easy


AUTHOR

Amarnath Murthy, Apr 20 2001


EXTENSIONS

More terms from Hieronymus Fischer, Jun 26 2007


STATUS

approved



