Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

127, 511, 2047, 8191, &c. And the series equal to the last term
of these numbers is 1+2+4+24+96+384, kc. For 1=1,
1+2=3, 1+2+4=7, 1+2+4+24=31; and so of the rest.
In which series it is remarkable, that each term after the first
three terms, viz after 1, 2, 4, is the + of the following term.
1
Thus 24 is the + of %; 96 is the i of 384; and 384 is the
of 1536; and so on.
After the first three terms likewise, if each term is multiplied
by 4, and 3 is added to the product, the sum will be the follow:
ing term. Thus 31 )