

A061107


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


8




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



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) 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:


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



KEYWORD

base,nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



