A100729 Period of the first difference of Ulam 1-additive sequence U(2,2n+1).

32, 26, 444, 1628, 5906, 80, 126960, 380882, 2097152, 1047588, 148814, 8951040, 5406720, 242, 127842440, 11419626400, 12885001946, 160159528116, 687195466408, 6390911336402, 11728121233408, 20104735604736

Offset

2,1

Comments

It was proved by Akeran that a(2^k-1) = 3^(k+1) - 1.

Note that a(n)=2^(2n+1) as soon as A100730(n)=2^(2n+3)-2, that happens for n=(m-2)/2 with m>=6 being an even element of A073639.

Links

Max Alekseyev, Table of n, a(n) for n = 2..31

M. Akeran, On some 1-additive sequences

J. Cassaigne and S. R. Finch, A class of 1-additive sequences and additive recurrences

S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.

Example

For k=2, we have a(3)=3^3-1=26.

Crossrefs

Cf. A100730 for the fundamental difference, A001857 for U(2, 3), A007300 for U(2, 5), A003668 for U(2, 7).

Cf. also A006844.

Sequence in context: A028697 A105701 A161885 * A070728 A070619 A070626

Adjacent sequences: A100726 A100727 A100728 * A100730 A100731 A100732

Keyword

nonn

Author

Ralf Stephan, Dec 03 2004

Extensions

a(3) corrected from 25 to 26 by Hugo van der Sanden and Bertram Felgenhauer (int-e(AT)gmx.de), Nov 11 2007

More terms from Balakrishnan V (balaji.iitm1(AT)gmail.com), Nov 15 2007

a(21..31) and b-file from Max Alekseyev, Dec 01 2007

Status

approved