This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334834 #34 May 24 2020 04:00:05 %S A334834 4,8,10,15,16,20,25,28,32,40,50,64,70,75,80,100,112,125,128,160,175, %T A334834 200,250,256,280,320,325,341,375,400,425,448,496,500,512,561,625,640, %U A334834 645,700,730,800,1000,1016,1024,1105,1120,1250,1280,1288,1387,1600,1729,1750 %N A334834 Composite numbers k such that the decimal expansion of ((1/2^(k-1))-1)/k is finite. %C A334834 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: %C A334834 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. %e A334834 10 is a term because ((1/2^9)-1)/10 = -0.0998046875; %e A334834 12 is not a term because ((1/2^11)-1)/12 = -0.08329264322916666666666... . %t A334834 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 *) %Y A334834 Cf. A001567 (Poulet numbers, a subsequence). %K A334834 nonn,base %O A334834 1,1 %A A334834 _Davide Rotondo_, May 13 2020 %E A334834 More terms from _Amiram Eldar_, May 14 2020