A197100 2*A197072(n-1) - A197072(n).

-3, -3, -5, 5, 1, 1, 13, -71, 47, 97, -65, 23, 73, -149, 719, -345, 2453, 299, 1737, 7851, 5359, 22021, 30039, 45211, 143627, 210871, 404681, 627271, 1446107, 2401465, 5033375, 8279849, 16695395, 30641101, 59192219, 107592545, 209720011, 386315899, 747523379

Offset

1,1

Comments

From A033844 it can be seen that prime(2^(n+1)) ~ 2*prime(2^n), which is explained by the prime number theorem. This led to the definition of A197072 (difference of these two expressions), which has again the property that A197072(n+1) ~ 2*A197072(n). This motivated the present sequence. (There is still a slow convergence to 2 of the ratio between successive terms here, e.g. a(55)/a(54) ~ 1.926.)

Links

Table of n, a(n) for n=1..39.

Prog

(PARI) a(n)=2*A197072(n-1)-A197072(n)

Crossrefs

Sequence in context: A087853 A095334 A071182 * A258642 A136027 A238371

Adjacent sequences: A197097 A197098 A197099 * A197101 A197102 A197103

Keyword

sign

Author

M. F. Hasler, Oct 10 2011

Status

approved