A144908 Composite numbers n such that sqrt(n) > A144907(n) and absolute normalized digital mean |dm(b, n) * 2 / (b - 1)| decreases for b in [2, k] for some k > 2.

32, 64, 125, 128, 192, 250, 256, 288, 343, 375, 384, 500, 512, 576, 640, 648, 768, 800, 896, 1024, 1029, 1125, 1152, 1280, 1296, 1536, 1568, 1600, 1715, 1792, 1875, 2025, 2048, 2058, 2304, 2401, 2500, 2560, 2592, 2816, 3072, 3136, 3200, 3328, 3375, 3456

Offset: 1

Author

Reikku Kulon, Sep 24 2008

Keywords

• base
• easy
• nonn

Comments

Subset of A144100.

Believed to have particular importance for linear congruential pseudorandom number generators.

Examples

			125 is a member: A144907(125) is 5, which is less than 11.18, the square root of 125;
125 in base 2 is 1111101; dm(2, 125) = (6 * 1 - 1) / 14 = 5/14 ~ 0.357;
125 in base 3 is 11122; dm(3, 125) = (3 * 0 + 2 * 2) / 10 = 2/5 = 0.4;
125 in base 4 is 1331; dm(4, 125) = (2 * -1 + 2 * 3) / 8 = 1/2 = 0.5;
5/14 * 2 / 1 = 5/7 ~ 0.714;
2/5 * 2 / 2 = 2/5 = 0.4;
1/2 * 2 / 3 = 1/3 ~ 0.333;
For b in [2, 4], |dm(b, 125) * 2 / (b - 1)| is decreasing.
		

Crossrefs

Cf. A144100, A144907, A144777