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

Author

Ralf Stephan, Dec 03 2004

Keywords

• nonn

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.

Examples

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

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.

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.

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