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%I #11 Oct 13 2022 13:48:23
%S 1,2,6,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,9,17,17,15,13,9,13,13,7,
%T 11,9,11,11,3,5,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,9,17,17,15,13,
%U 9,13,13,7,11,9,11,11,3,5,9,17,17,15,13,9,13,13,7
%N Sum three last digits to get next term of the sequence, starting 1,2,6.
%C Start with {1,2,6}:
%C {1,2,6,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,... which has period {9,17,17,15,13,9,13,13,7,11,9,11,11,3,5}.
%C Apparently sequences with any three initial digits become periodic:
%C 1,2,3,6,11,8,10,9,10,10,1,2,3,6,11,8,10,9,10,10,... period {1,2,3,6,11,8,10,9,10,10};
%C 1,2,4,7,13,11,5,7,13,11,5,... period {7,13,11,5};
%C 8,9,7,24,13,8,12,11,4,6,11,8,10,9,10,10,1,2,3,6,11,8,10,9,10,10,... period {1,2,3,6,11,8,10,9,10,10};
%C 4,4,4,12,7,10,8,9,17,17,15,13,9,13,13,7,11,9,11,11,3,5,... period {9,17,17,15,13,9,13,13,7,11,9,11,11,3,5}, etc.
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%t s={1,2,6};dd={1,2,6};Do[a=dd[[-1]]+dd[[-2]]+dd[[-3]];AppendTo[s,a];dd=Flatten[{dd,IntegerDigits[s]}],{100}];s
%t nxt[{a_,b_,c_}]:={b,c,Total[Take[Flatten[IntegerDigits/@{a,b,c}],-3]]}; Transpose[ NestList[ nxt,{1,2,6},100]][[1]] (* _Harvey P. Dale_, Feb 01 2015 *)
%Y Cf. A254056.
%K nonn,base,easy
%O 1,2
%A _Zak Seidov_, Jan 24 2015
%E More terms from _Harvey P. Dale_, Feb 01 2015
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