Keith number

In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a number in the following integer sequence:

Keith numbers were introduced by Mike Keith in 1987. They are computationally very challenging to find, with only about 100 known.

Introduction

To determine whether an n-digit number N is a Keith number, create a Fibonacci-like sequence that starts with the n decimal digits of N, putting the most significant digit first. Then continue the sequence, where each subsequent term is the sum of the previous n terms. By definition, N is a Keith number if N appears in the sequence thus constructed.

As an example, consider the 3-digit number N = 197. The sequence goes like this:

Because 197 appears in the sequence, 197 is seen to be indeed a Keith number.

Definition

A Keith number is a positive integer N that appears as a term in a linear recurrence relation with initial terms based on its own decimal digits. Given an n-digit number

a sequence is formed with initial terms and with a general term produced as the sum of the previous n terms. If the number N appears in the sequence , then N is said to be a Keith number. One-digit numbers possess the Keith property trivially, and are usually excluded.

Keith Urban

Keith Lionel Urban (born 26 October 1967) is a New Zealand-born Australian country music singer, songwriter, guitarist, entrepreneur, and music competition judge. In 1991, he released a self-titled debut album and charted four singles in Australia before moving to the United States the following year. He found work as a session guitarist before starting a band known as The Ranch, which recorded one studio album on Capitol Nashville and charted two singles on the Billboard Hot Country Songs chart.

Still signed to Capitol, Urban made his solo American debut in 1999 with the album Keith Urban. Certified platinum in the US, it produced his first number one on Hot Country Songs with "But for the Grace of God". "Somebody Like You", the first single from his second Capitol album, Golden Road (2002), was named by Billboard as the biggest country hit of the 2000s decade. The album's fourth single, "You'll Think of Me", earned him his first Grammy. 2004's Be Here, his third American album, produced three more number 1 singles and became his highest-selling album, earning 4× Platinum certification. Love, Pain & the Whole Crazy Thing was released in 2006, containing "Once in a Lifetime" as well as his second Grammy song, "Stupid Boy". A greatest hits package entitled Greatest Hits: 18 Kids followed in late-2007. Defying Gravity and Get Closer were released on March 31, 2009 and November 16, 2010 respectively. In September 2013, he released a brand new album titled Fuse, which produced four more number ones on the newly introduced Country Airplay chart, two of which are duets with Miranda Lambert and Eric Church. A new single, entitled "John Cougar, John Deere, John 3:16", was released in June 2015 as the lead-off single to his upcoming eighth American studio album Ripcord.

Keith Sweat

Keith Sweat (born July 22, 1961) is an American R&B/soul, singer-songwriter, record producer, actor, radio personality, and an innovator of new jack swing.

Biography

Keith Sweat was born in Harlem, New York to Juanita Sweat, a hairdresser, and Charles Crier (died 1973), a factory worker. Juanita raised their five children alone after Crier's death. He worked as a night stock boy at Macy's and then a mailroom clerk at Paine Webber. In just four years he worked his way up to a lucrative brokerage assistant job on the floor of the New York Stock Exchange. Sweat worked for the commodities market in the New York Mercantile Exchange. Sweat sang at nightclubs throughout New York City until he was discovered and offered a recording contract with Elektra Records in 1987.

He has three daughters. He named his record label, Keia Entertainment, after his younger daughter. From 1992 until 2002, he was married to The Real Housewives of Atlanta co-star Lisa Wu Hartwell. With her, he had two sons Jordan (b. 1995) and Justin (b. 1998)

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