A334834 Composite numbers k such that the decimal expansion of ((1/2^(k-1))-1)/k is finite.

4, 8, 10, 15, 16, 20, 25, 28, 32, 40, 50, 64, 70, 75, 80, 100, 112, 125, 128, 160, 175, 200, 250, 256, 280, 320, 325, 341, 375, 400, 425, 448, 496, 500, 512, 561, 625, 640, 645, 700, 730, 800, 1000, 1016, 1024, 1105, 1120, 1250, 1280, 1288, 1387, 1600, 1729, 1750

Offset: 1

Author

Davide Rotondo, May 13 2020

Keywords

• nonn
• base

Comments

If (1/2^(n-1))-1 divided by n results in a finite decimal number, n is prime or pseudoprime. Poulet numbers: A001567 are a subsequence:

if n|(2^(n-1)-1) then the denominator of ((1/2^(n-1))-1)/n is a power of 2, so the decimal expansion of the fraction is finite. (1/2^n)-1 is < 0 for n >= 1.

Examples

			10 is a term because ((1/2^9)-1)/10 = -0.0998046875;
12 is not a term because ((1/2^11)-1)/12 = -0.08329264322916666666666... .
		

Crossrefs

Cf. A001567 (Poulet numbers, a subsequence).

Programs

Mathematica

A003592Q[n_] := n/2^IntegerExponent[n, 2]/5^IntegerExponent[n, 5] == 1; seqQ[n_] := CompositeQ[n] && A003592Q[Denominator[((1/2^(n - 1)) - 1)/n]]; Select[Range[2000], seqQ] (* Amiram Eldar, May 14 2020 *)

Extensions

More terms from Amiram Eldar, May 14 2020