A TRIBONACCI-LIKE SEQUENCE OF COMPOSITE NUMBERS

摘要

We find three positive integers x_o,x_1,x_2 satisfying gcd(x_0,x_1,x_2) = 1 such that the tribonacci-like sequence (x_n)∞_n=0 given by x_(n+1) = + x_(n-1) + x_(n-2) for n≥2 consists of composite numbers only. The initial values are x_o = 99202581681909167232, x_1 = 67600144946390082339, x_2 = 139344212815127987596. This is a natural extension of a similar result of Graham for the Fibonacci-like sequence.