[seqfan] 3, 21, 25

[Tomasz Ordowski]

Dear SeqFans!

Let us define:

Odd numbers n = k1 2^m1 + 1 = k2 2^m2 - 1 with k1 and k2 odd
such that k1 + 2^m1 = |k2 - 2^m2|. This is a strong condition.

Amiram Eldar only found {3, 21, 25} and no more n < 10^8.
Is this set complete or is it worth doing further research?

3 = 1*2+1 = 1*2^2-1 and 1+2 = |1-2^2| = 3,
21 = 5*2^2+1 = 11*2-1 and 5+2^2 = |11-2| = 9,
25 = 3*2^3+1 = 13*2-1 and 3+2^3 = |13-2| = 11.

Best regards,

Thomas Ordowski
___________________________
By the way, let's define similarly:
Odd numbers n = k1 2^m1 + 1 = k2 2^m2 - 1 with k1 and k2 odd
such that k1 + 2^m1 = k2 + 2^m2. A slightly different condition.
Such numbers n < 10^8 (less interesting to me) are {5, 11},
which was also checked by Ami. Thanks!
5 = 1*2^2+1 = 3*2-1 and 1+2^2 = 3+2 = 5,
11 = 5*2+1 = 3*2^2-1 and 5+2 = 3+2^2 = 7.