Problem: I was wondering if anyone could help me with finding a continous function (with 5 or fewer constants) that will generate the series 35, 45, 60, y , 120, 180, 280, 450, 744, 1260 as x assumes the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 SPOILER SPOILER From - Thu Feb 12 10:17:35 1998 From: pmontgom@cwi.nl (Peter L. Montgomery) Subject: Re: Number Problem for Experts Organization: CWI, Amsterdam > I was wondering if anyone could help me with finding a continous > function (with 5 or fewer constants) that will generate the series > 35, 45, 60, y , 120, 180, 280, 450, 744, 1260 as x assumes the values > 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 > Also, i need to find the value of y in terms of standard functions. All prime divisors of the supplied numbers are below 10, except the divisor 31 of 744. I observe that 31 = 2^5 - 1, and that 2^6 - 1 = 63 divides 1260. This pattern persists in the other direction, since 15 divies 450 and 7 divides 280. Look at the quotients y/(2^(x-4) - 1): x 1 2 3 4 5 6 7 8 9 10 y 35 45 60 ? 120 180 280 450 744 1260 2^(x-4)-1 -7/8 -3/4 -1/2 0 1 3 7 15 31 63 quotient -40 -60 -120 ? 120 60 40 30 24 20 The largest prime divisor in the quotient row is 5. There is a simple formula for this row, which I'll leave to the reader. If we extend our formula to non-integral values, we guess an irrational value near 83 for y when x = 4. -- Peter-Lawrence.Montgomery@cwi.nl San Rafael, California A mathematician whose age has doubled since he last drove an automobile.