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%I #9 Apr 03 2023 10:36:10
%S 0,1,1,2,3,5,8,3,2,6,8,4,3,8,1,10,1,2,4,6,0,7,7,4,2,7,9,6,6,3,10,3,4,
%T 8,2,1,4,5,9,4,4,9,3,3,7,0,8,8,6,5,2,8,0,9,9,8,8,7,6,4,1,6,7,3,1,5,6,
%U 1,8,9,7,7,5,3,9,2,2,5,7,2,10,2,3,6,9,5,5,1,7,8,5,4,10,4,5,10,5,6,2,9,1,1
%N Fibonacci sequence (A000045) mod 10 with carry.
%C Observation (from Kaprekar) this sequence can be the reverse of 1/109 (A021113) which is recuring and has a period of 108 digits:
%C 0.[009174311926605504587155963302752293577981651376146788
%C 990825688073394495412844036697247706422018348623853211]. - _Eric Desbiaux_, Oct 28 2008
%H Primes.utm.edu, <a href="https://t5k.org/curios/page.php/109.html">Sum of 11^n*10^n</a> [From _Eric Desbiaux_, Oct 28 2008]
%t f[0] = 0; f[1] = f[2] = 1; f[n_] := f[n] = Block[{k}, If[f[n - 2] + f[n - 3] >= 10, k = 1, k = 0]; Mod[f[n - 1] + f[n - 2], 10] + k]; Table[ f[n], {n, 0, 100} ]
%Y Cf. A000045.
%K easy,nonn
%O 0,4
%A _Robert G. Wilson v_, Oct 17 2001
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