OFFSET
1,2
COMMENTS
Subset of A017910.
The corresponding Mersenne number exponents are given by A144931.
From Gil Broussard, Sep 12 2009: (Start)
It appears that the terms of this sequence are the only numbers with this property: the binary expansion of a(n) is identical to the first ceiling(log_2(a(n))) nonzero digits of the binary expansion of 1/a(n). In other words, if the binary expansion of a(n) is 6 digits, then the first 6 nonzero digits of the binary expansion of 1/a(n) is identical for some a(n).
For example:
a(2)=11=binary 1011 which is 4 digits long and equivalent to the first 4 digits of its binary reciprocal (after the initial zeros):
1/a(2) = binary .000[1011]101000101110100010111010...
Table of a(2) to a(11):
11 1011 -> .000[1011]1010001011101000101110100010111010001011...
45 101101 -> .00000[101101]100000101101100000101101100000101101...
181 10110101 -> .0000000[10110101]00001001111001101000101010011011...
362 101101010 -> .00000000[101101010]000100111100110100010101001101...
724 1011010100 -> .000000000[1011010100]0010011110011010001010100110...
1448 10110101000 -> .0000000000[10110101000]01001111001101000101010011...
2896 101101010000 -> .00000000000[101101010000]100111100110100010101001...
11585 10110101000001 -> .0000000000000[10110101000001]01111001100110100100...
23170 101101010000010 -> .00000000000000[101101010000010]111100110011010010...
741455 10110101000001001111 -> .0000000000000000000[10110101000001001111]01100110...
(End)
PROG
(PARI) forstep(m=1, 10^6, 2, n=sqrtint(2^m-1); if(2^m-1-n^2<n, print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Reikku Kulon, Sep 25 2008
EXTENSIONS
Edited by Max Alekseyev, Oct 12 2009
Edited by Charles R Greathouse IV, Mar 23 2010
STATUS
approved