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A254057
Sum three last digits to get next term of the sequence, starting 1,2,6.
0
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, 9, 17, 17, 15, 13, 9, 13, 13, 7, 11, 9, 11, 11, 3, 5, 9, 17, 17, 15, 13, 9, 13, 13, 7
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.
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
Cf. A254056.
Sequence in context: A347535 A354975 A280228 * A257083 A054974 A072481
KEYWORD
nonn,base,easy
AUTHOR
Zak Seidov, Jan 24 2015
EXTENSIONS
More terms from Harvey P. Dale, Feb 01 2015
STATUS
approved