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A186830 Keith sequence for the number 197. 2
1, 9, 7, 17, 33, 57, 107, 197, 361, 665, 1223, 2249, 4137, 7609, 13995, 25741, 47345, 87081, 160167, 294593, 541841, 996601, 1833035, 3371477, 6201113, 11405625, 20978215, 38584953, 70968793, 130531961 (list; graph; refs; listen; history; text; internal format)
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. - From Alonso del Arte, Mar 14 2011

REFERENCES

Martin Klazar and Florian Luca, Counting Keith Numbers, Journal of Integer Sequences, Vol. 10 (2007), #07.2.2.

LINKS

Table of n, a(n) for n=1..30.

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

Cf. A007629.

Sequence in context: A268228 A131724 A190995 * A124050 A107663 A231605

Adjacent sequences:  A186827 A186828 A186829 * A186831 A186832 A186833

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane, Feb 27 2011

STATUS

approved

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Last modified March 24 00:37 EDT 2017. Contains 283984 sequences.