A254057 Sum three last digits to get next term of the sequence, starting 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, 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.

Links

Table of n, a(n) for n=1..72.

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

Cf. A254056.

Sequence in context: A347535 A354975 A280228 * A257083 A054974 A072481

Adjacent sequences: A254054 A254055 A254056 * A254058 A254059 A254060

Keyword

nonn,base,easy

Author

Zak Seidov, Jan 24 2015

Extensions

More terms from Harvey P. Dale, Feb 01 2015

Status

approved