OFFSET
1,2
COMMENTS
This sequence illustrates why 197 is a Keith number (cf. A007629).
Other multiples of 197 in the sequence are 4137 and 992207243244533. - Alonso del Arte, Mar 14 2011
LINKS
M. Klazar and F. Luca, Counting Keith numbers, Journal of Integer Sequences, Vol. 10 (2007), #07.2.2.
Eric Weisstein's World of Mathematics, Keith Number
Index entries for linear recurrences with constant coefficients, signature (1,1,1).
FORMULA
a(1)=1, a(2)=9, a(3)=7; thereafter a(n) = sum of previous three terms. Note that 197 appears in the sequence, which is why 197 is a Keith number.
G.f.: x*(1+8*x-3*x^2)/(1-x-x^2-x^3). [Colin Barker, Jun 19 2012]
MATHEMATICA
keithSeq[n_Integer, b_:10, goBeyondN_:0] := Module[{seq = IntegerDigits[n, b], ord, max = n + goBeyondN, curr}, ord = Length[seq]; curr = seq[[-1]]; While[curr < max, curr = Plus@@Take[seq, -ord]; seq = Append[seq, curr]]; Return[seq]]; keithSeq[197, 10, 10^8] (* Alonso del Arte, Mar 14 2011 *)
PROG
(PARI) Vec((1+8*x-3*x^2)/(1-x-x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Feb 04 2013
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 27 2011
STATUS
approved