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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 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
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
Sequence in context: A008963 A031324 A226251 * A093092 A031111 A089911
KEYWORD
nonn,base,easy
AUTHOR
Bodo Zinser, Mar 20 2004
EXTENSIONS
Edited by N. J. A. Sloane, Mar 20 2010
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)