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A Keith number is an n-digit integer N>9 such that if a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed with the first n terms taken as the decimal digits of the number N, then N itself occurs as a term in the sequence. For example, 197 is a Keith number since it generates the sequence 1, 9, 7, 1+9+7=17, 9+7+17=33, 7+17+33=57, 17+33+57=107, 33+57+107=197, ... (Keith). There is no known general technique for finding Keith numbers except by exhaustive search. Keith numbers are much rarer than the primes, with only 84 Keith numbers with <26 digits. The first few are 14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, ... |

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import java.util.Scanner; public class keith { private static Scanner sc = new Scanner(System.in); int n, ar[], l; public void input() { System.out.println("Enter a number:"); n = sc.nextInt(); int x = n; l=0; while(x!=0) { x = x/10; l++; } ar = new int[l]; } public boolean check() { int sum=0, x=n, i; for(i=l-1;i>=0;i--) { ar[i]=x%10; sum = sum+x%10; x = x/10; } while(sum<=n) { for(i=0;i<l-1;i++) { ar[i] = ar[i+1]; } ar[l-1]=sum; sum=0; for(i=0;i<l;i++) { sum = sum+ar[i]; } if(sum==n) return true; } return false; } public static void main() { keith kt = new keith(); kt.input(); if(kt.check()) { System.out.println("The number is a keith number."); } else { System.out.println("The number is not a keith number."); } } } |

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