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Sum two last digits of the sequence to get next term, starting with 1,2.
1

%I #7 Jan 25 2015 21:24:39

%S 1,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,2,3,5,8,13,4,

%T 7,11,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11

%N Sum two last digits of the sequence to get next term, starting with 1,2.

%C Start with {1,2}: 1,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,11,2,3,5,8,13,4,7,... period {11,2,3,5,8,13,4,7,}.

%C Sequences with any other pair of initial digits eventually merge with case {1,2} except for the case {4,5}: 4,5,9,14,5,9,14,5,9,14,... which has period {5,9,14}.

%t a=1;b=2;s={a,b};dd={a,b};Do[a=dd[[-1]]+dd[[-2]];AppendTo[s,a];dd=Flatten[{dd,IntegerDigits[s]}],{20}];s

%K nonn,base

%O 1,2

%A _Zak Seidov_, Jan 24 2015