Keith number


Given a base b integer

n=i=1kdibi-1

where d1 is the least significant digit and dk is the most significant, construct the sequence a1=dk,ak=d1, and for m>k,

am=i=1kam-i.

If there is an x such that ax=n, then n is a Keith number or repfigit number.

In base 10, the first few Keith numbers below ten thousand are: 14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909 (see A007629 in Sloane’s OEIS for a longer listing). 47 is a base 10 Keith number because it is contained the Fibonacci-like recurrence started from its base 10 digits: 4, 7, 11, 18, 29, 47, etc.

References

  • 1 M. Keith, “Repfigit Numbers” J. Rec. Math. 19 (1987), 41 - 42.
Title Keith number
Canonical name KeithNumber
Date of creation 2013-03-22 16:00:20
Last modified on 2013-03-22 16:00:20
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A63
Synonym repfigit number