Keith number
Encyclopedia : K : KE : KEI : Keith number
In mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is an integer that appears as a term in a linear recurrence relation with initial terms based on its own digits. Given an n-digit number
[N=\sum_^ 10^i ,]
a sequence [S_N] is formed with initial terms [d_, d_,\ldots, d_1, d_0] and with a general term produced as the sum of the previous n terms. If the number N appears in the sequence [S_N], then N is said to be a Keith number.
For example, taking 197 in such a way creates the sequence [1, 9, 7, 17, 33, 57, 107, 197, \ldots]. The first few Keith numbers are:
14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909 (sequence in OEIS)
Whether or not there are infinitely many Keith numbers is currently a matter of speculation. There are only 71 Keith numbers below 1019, making them much rarer than prime numbers.
Mike Keith is a mathematician who published a paper on these numbers titled "Repfigit Numbers" in a 1987 issue of the Journal of Recreational Mathematics.
External links
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.