A051179 -id:A051179 - cp's OEIS frontend

A116213 (2^(2^(2^n))-1)/(2^(2^n)+1).

1, 3, 3855, 450552876409790643671482431940419874915447411150352389258589821042463539455

Offset: 0

Alexander Adamchuk, Apr 08 2007

nonn

2^n+1 divides 2^(2^n)-1 iff n is a power of 2.

Cf. A000215 = Fermat numbers: 2^(2^n)+1. Cf. A051179 = 2^(2^n)-1.

Table[ (2^2^2^n - 1) / (2^2^n + 1), {n,0,3} ]

a(n) = (2^(2^(2^n))-1)/(2^(2^n)+1). a(n) = A051179(2^n)/A000215(n).

A116961 Numbers of the form 2^(2^k-1)-1, 2^(2^k-1), 2^(2^k)-1, 2^(2^k).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 15, 16, 127, 128, 255, 256, 32767, 32768, 65535, 65536, 2147483647, 2147483648, 4294967295, 4294967296, 9223372036854775807, 9223372036854775808, 18446744073709551615, 18446744073709551616

Offset: 1

Henrik Lundquist (sploinker(AT)sploink.dk), Mar 30 2006

nonn

The values are important in binary computer arithmetic.

Cf. A001146, A051179, A058891, A077585.

Edited by Don Reble, Mar 31 2006

A162647 Numerators associated with denominators A000215(n) approximating the complementary Thue-Morse constant.

Original entry on oeis.org

2, 3, 10, 151, 38506, 2523490711, 10838310072981296746, 199931532107794273605284333428918544791, 68033174967769840440887906939858451149105560803546820641877549596291376780906

Offset: 0

Vladimir Shevelev, Jul 08 2009, Jul 14 2009

If in the sequence of numbers N for which A010060(N+2^n)=1-A010060(N) the odious (evil) terms are
replaced by 1's (0's), we obtain a 2^(n+1)-periodic binary sequence. These are the post-period
binary (base-2) digits of the complementary Thue-Morse constant 1-A014571 = 0.58754596635989240221663...,
which has a continued fraction and convergents 3/5, 7/12, 10/17, 47/80, 151/257, 801/1365,...
The a(n) are numerators of the convergents selected with denominators taken from A000215.

V. Shevelev, Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence, arXiv:0907.0880

Cf. A010060, A000215, A085394, A085395, A081706, A161627, A161639, A162634.

a(n)=A000215(n)-A162634(n). For n>=1, a(n+1)=1+(2^(2^n)-1)*a(n) = 1+A051179(n)*a(n).

Edited by R. J. Mathar, Sep 23 2009

cp's OEIS Frontend

A116213 (2^(2^(2^n))-1)/(2^(2^n)+1).

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A116961 Numbers of the form 2^(2^k-1)-1, 2^(2^k-1), 2^(2^k)-1, 2^(2^k).

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A162647 Numerators associated with denominators A000215(n) approximating the complementary Thue-Morse constant.

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