A254522 Numerators of (2^n - 1 + (-1)^n)/(2*n), n > 0.

0, 1, 1, 2, 3, 16, 9, 16, 85, 256, 93, 512, 315, 4096, 5461, 2048, 3855, 65536, 13797, 131072, 349525, 1048576, 182361, 1048576, 3355443, 16777216, 22369621, 33554432, 9256395, 268435456, 34636833, 67108864, 1431655765, 4294967296, 17179869183, 8589934592, 1857283155, 68719476736, 91625968981

Offset: 1

Author

Paul Curtz, Jan 31 2015

Keywords

• nonn

Comments

An autosequence of the first kind is a sequence which main diagonal is A000004.

Difference table of a(n)/A093803(n):

0, 1, 1, 2, 3, 16/3, ...

1, 0, 1, 1, 7/3, 11/3, ...

-1, 1, 0, 4/3, 4/3, 10/3, ...

2, -1, 4/3, 0, 2, 2, ...

-3, 7/3, -4/3, 2, 0, 16/5, ...

16/3, -11/3, 10/3, -2, 16/5, 0, ...

etc.

This is an autosequence of the first kind.

Its first (or second) upper diagonal is A075101(n)/(2*A000265(n)).

From Robert Israel, Apr 03 2017: (Start)

If p is a prime == 5 (mod 8), then a(5*p) = (2^(5*p-1)-1)/5 and a(5*p+3) = 2^(5*p) = 10*a(5*p)+2. This explains pairs such as

a(25) = 3355443

a(28) = 33554432

and

a(65) = 3689348814741910323

a(68) = 36893488147419103232. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..3321

Crossrefs

Cf. A000004, A075101, A093803, A099430.

Programs

Maple

seq(numer((2^n-1+(-1)^n)/(2*n)), n=1..50); # Robert Israel, Feb 01 2015

Mathematica

Table[Numerator[(2^n - 1 + (-1)^n)/(2*n)], {n, 39}] (* Michael De Vlieger, Feb 01 2015 *)

Extensions

a(25) corrected by Robert Israel, Apr 03 2017