cp's OEIS Frontend

A204983 a(n) = 2^(k-1)-2^(j-1), where (2^(k-1),2^(j-1)) is the least pair of distinct positive powers of 2 for which n divides 2^(k-1)-2^(j-1).

%I A204983 #26 Oct 03 2023 10:32:22
%S A204983 1,2,3,4,15,6,7,8,63,30,1023,12,4095,14,15,16,255,126,262143,60,63,
%T A204983 2046,2047,24,1048575,8190,262143,28,268435455,30,31,32,1023,510,4095,
%U A204983 252,68719476735,524286,4095,120,1048575,126,16383,4092,4095
%N A204983 a(n) = 2^(k-1)-2^(j-1), where (2^(k-1),2^(j-1)) is the least pair of distinct positive powers of 2 for which n divides 2^(k-1)-2^(j-1).
%C A204983 For a guide to related sequences, see A204892.
%C A204983 (Conjecture) Equivalently, the solution set of 2^p * (2^q - 1) = x * y, OR 2^q - 1 = 2^p * x * y, for at most one of the naturals x and y being given; unknown p and q in the integers; then a(n) = 2^p * (2^q - 1) where p and q are directly related to n (see formula). - _Andrew T. Porter_, Dec 20 2022
%F A204983 Conjecture: a(n) = 2^A007814(n) * (2^A007733(n) - 1). - _Andrew T. Porter_, Dec 20 2022
%t A204983 (See the program at A204979.)
%o A204983 (PARI) a(n) = for (k=1, oo, for (j=1, k-1, my(d=2^(k-1)-2^(j-1)); if (!(d % n), return(d)););); \\ _Michel Marcus_, Sep 16 2023
%Y A204983 Cf. A204979, A204892, A204984.
%Y A204983 Cf. A000079, A173787.
%Y A204983 Cf. A007733, A007814.
%K A204983 nonn
%O A204983 1,2
%A A204983 _Clark Kimberling_, Jan 21 2012