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%I #6 Oct 13 2014 10:29:15
%S 1,2,3,5,8,13,9,10,9,9,18,10,8,8,16,9,10,9,9,18,10,8,8,16
%N Sum of the largest and least digits of two previous terms: a(n) is a sum of the largest and least digits of a(n-1) and a(n-2).
%C The sequence ends with three types of cycle, depending on seed terms a(1) and a(2): p1={9,10,9,9,18,10,8,8,16}, p2={10,5,5}, p3={10,7,7,14,8,9,17}. (At a(1)=a(2)=0 all terms of the sequence, s00, are zero.)
%C Denote by smn the sequence starting with a(1)=m, a(2)=n, then some sequences are: s02=0,2,2,4,6,10,6,6,12,7,8,15,p1 s03=0,3,3,6,9,15,p2 s12=1,2,3,5,8,13,p1 s07=0,7,7,14,8,9,17,p3 s27=2,7,9,16,10,6,6,12,7,8,15,p1 s49=4,9,13,10,3,3,6,9,15,p2 s67=6,7,13,8,9,17,p3. From 54 different nontrivial sequences with seeds from 0,1 to 9,9, 35 sequences end with p1, 8 with p2 and 11 with p3.
%F a(n>2)=Maxdigit[a(n-1), a(n-2)]+Mindigit[a(n-1), a(n-2)], a(1)=1, a(2)=2
%t nxt[{a_,b_}]:=Module[{d=Flatten[IntegerDigits/@{a,b}]},{b,Max[d]+ Min[d]}]; Transpose[NestList[nxt,{1,2},10]][[1]] (* _Harvey P. Dale_, Oct 13 2014 *)
%K base,nonn
%O 1,2
%A _Zak Seidov_, Mar 19 2005
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