A093086 "Fibonacci in digits": start with a(0)=0, a(1)=1; repeatedly adjoin the digits of the sum of the next two terms.
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
Examples
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.
Links
- Hakan Icoz, Table of n, a(n) for n = 0..20000
Programs
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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
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Mathematica
Fold[Join[#, IntegerDigits[Total[#[[#2;; #2+1]]]]] &, {0, 1}, Range[100]] (* Paolo Xausa, Aug 18 2025 *)
Extensions
Edited by N. J. A. Sloane, Mar 20 2010
Comments