OFFSET
2,1
COMMENTS
Keith numbers are described in A007629. It appears that a(n) < 2n. If n or n+1 is a Fibonacci number f, then a(n) = f. If n>3 and n+2 is a Fibonacci number f, then a(n) = f. The graph shows that 2n-1, 3n/2-1, and 8(n-5)/7+5 are frequent values of a(n).
LINKS
T. D. Noe, Table of n, a(n) for n = 2..1000
MATHEMATICA
IsKeith[n_, b_] := Module[{d, s, k}, d = IntegerDigits[n, b]; s = Total[d]; k = 1; While[AppendTo[d, s]; s = 2 s - d[[k]]; s < n, k++]; s == n]; Table[k = n; While[! IsKeith[k, n], k++]; k, {n, 2, 100}]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
T. D. Noe, Mar 24 2011
STATUS
approved