OFFSET
1,2
COMMENTS
Start with {1,2,6}:
{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}.
Apparently sequences with any three initial digits become periodic:
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};
1,2,4,7,13,11,5,7,13,11,5,... period {7,13,11,5};
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};
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
MATHEMATICA
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
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 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Zak Seidov, Jan 24 2015
EXTENSIONS
More terms from Harvey P. Dale, Feb 01 2015
STATUS
approved