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A093086
"Fibonacci in digits": start with a(0)=0, a(1)=1; repeatedly adjoin the digits of the sum of the next two terms.
15
0, 1, 1, 2, 3, 5, 8, 1, 3, 9, 4, 1, 2, 1, 3, 5, 3, 3, 4, 8, 8, 6, 7, 1, 2, 1, 6, 1, 4, 1, 3, 8, 3, 3, 7, 7, 5, 5, 4, 1, 1, 1, 1, 6, 1, 0, 1, 4, 1, 2, 1, 0, 9, 5, 2, 2, 2, 7, 7, 1, 1, 5, 5, 3, 3, 1, 9, 1, 4, 7, 4, 4, 9, 1, 4, 8, 2, 6, 1, 0, 8, 6, 4, 1, 0, 1, 0, 5, 1, 1, 1, 1, 8, 1, 3, 1, 0, 5, 1, 2, 1, 0, 8, 7, 1, 8
OFFSET
0,4
COMMENTS
Formally, define strings of digits S_i as follows. S_0={0}, S_1={0,1}. For n >= 1, let S_n={t_0, t_1, ..., t_z}. Then S_{n+1} is obtained by adjoining the digits of t_{n-1}+t_n to S_n. The sequence gives the limiting string S_oo.
All digits appear infinitely often, although the sequence is not periodic.
EXAMPLE
After S_6 = {0,1,1,2,3,5,8} we have 5+8 = 13, so we get
S_7 = {0,1,1,2,3,5,8,1,3}. Then 8+1 = 9, so we get
S_8 = {0,1,1,2,3,5,8,1,3,9}. Then 1+3 = 4, so we get
S_9 = {0,1,1,2,3,5,8,1,3,9,4}, and so on.
MAPLE
with(linalg): A:=matrix(1, 2, [0, 1]): for n from 1 to 100 do if A[1, n]+A[1, n+1]<10 then A:=concat(A, matrix(1, 1, A[1, n]+A[1, n+1])) else A:=concat(A, matrix(1, 2, [1, A[1, n]+A[1, n+1]-10])) fi od: matrix(A); # Emeric Deutsch, May 31 2005
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Bodo Zinser, Mar 20 2004
EXTENSIONS
Edited by N. J. A. Sloane, Mar 20 2010
STATUS
approved