OFFSET
1,2
COMMENTS
The integers k for which the equation 2^x - k = k*2^y - 1 has a solution x,y > 0.
If x,y > 0, then 2^y + 1 divides 2^x + 1 if and only if x/y is odd.
The prime numbers of this sequence are A281728.
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..1000
EXAMPLE
(2^5+1)/(2^1+1) = 11 = 1011,
(2^10+1)/(2^2+1) = 205 = 11001101,
(2^15+1)/(2^3+1) = 3641 = 111000111001,
(2^20+1)/(2^4+1) = 61681 = 1111000011110001,
(2^25+1)/(2^5+1) = 1016801 = 11111000001111100001,
(2^30+1)/(2^6+1) = 16519105 = 111111000000111111000001,
(2^35+1)/(2^7+1) = 266354561 = 1111111000000011111110000001, ...
Note that all the above examples are A020518(n) for n > 0.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Feb 16 2024
EXTENSIONS
More terms from Michel Marcus, Feb 17 2024
STATUS
approved