cp's OEIS Frontend

A370425 Integers of the form (2^x + 1) / (2^y + 1).

%I A370425 #8 Feb 18 2024 11:38:04
%S A370425 1,3,11,13,43,57,171,205,241,683,993,2731,3277,3641,4033,10923,16257,
%T A370425 43691,52429,61681,65281,174763,233017,261633,699051,838861,1016801,
%U A370425 1047553,2796203,4192257,11184811,13421773,14913081,15790321,16519105,16773121,44739243,67100673,178956971
%N A370425 Integers of the form (2^x + 1) / (2^y + 1).
%C A370425 The integers k for which the equation 2^x - k = k*2^y - 1 has a solution x,y > 0.
%C A370425 If x,y > 0, then 2^y + 1 divides 2^x + 1 if and only if x/y is odd.
%C A370425 The prime numbers of this sequence are A281728.
%H A370425 Max Alekseyev, <a href="/A370425/b370425.txt">Table of n, a(n) for n = 1..1000</a>
%e A370425 (2^5+1)/(2^1+1) = 11 = 1011,
%e A370425 (2^10+1)/(2^2+1) = 205 = 11001101,
%e A370425 (2^15+1)/(2^3+1) = 3641 = 111000111001,
%e A370425 (2^20+1)/(2^4+1) = 61681 = 1111000011110001,
%e A370425 (2^25+1)/(2^5+1) = 1016801 = 11111000001111100001,
%e A370425 (2^30+1)/(2^6+1) = 16519105 = 111111000000111111000001,
%e A370425 (2^35+1)/(2^7+1) = 266354561 = 1111111000000011111110000001, ...
%e A370425 Note that all the above examples are A020518(n) for n > 0.
%o A370425 (PARI) get_xy(m) = my(x, y, t); y=valuation(m-1, 2); t=m*(2^y+1)-1; if(t!=2^(x=valuation(t, 2)), [], [x, y]); \\ _Max Alekseyev_, Feb 18 2024
%Y A370425 Cf. A064896 (integers of the form (2^x-1)/(2^y-1)), A079665, A281728.
%K A370425 nonn
%O A370425 1,2
%A A370425 _Thomas Ordowski_, Feb 16 2024
%E A370425 More terms from _Michel Marcus_, Feb 17 2024