A188201 The least base-n Keith number >= n.

2, 3, 5, 5, 8, 8, 8, 17, 14, 13, 13, 13, 20, 18, 23, 33, 26, 21, 21, 21, 32, 28, 35, 49, 29, 33, 41, 57, 44, 38, 34, 34, 34, 43, 53, 73, 56, 48, 45, 81, 62, 53, 47, 89, 68, 53, 71, 97, 74, 63, 77, 55, 55, 55, 60, 113, 86, 73, 89, 69, 92, 78, 95, 129, 98, 83, 73, 137, 104, 88

Offset: 2

Author

T. D. Noe, Mar 24 2011

Keywords

• nonn
• base

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

Crossrefs

Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188195-A188200.

Programs

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}]