A107684 Union of sequences 2^k-1, 2^k and 2^k+1.

0, 1, 2, 3, 4, 5, 7, 8, 9, 15, 16, 17, 31, 32, 33, 63, 64, 65, 127, 128, 129, 255, 256, 257, 511, 512, 513, 1023, 1024, 1025, 2047, 2048, 2049, 4095, 4096, 4097, 8191, 8192, 8193, 16383, 16384, 16385, 32767, 32768, 32769, 65535, 65536, 65537, 131071

Offset: 0

Author

Reinhard Zumkeller, May 20 2005

Keywords

• nonn

Comments

Subsequence of A107686.

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,-1,2,2,2).

Crossrefs

Cf. A000225, A000079, A000051.

Programs

Mathematica

Flatten[{#-1,#,#+1}&/@(2^Range[0,20])]//Union (* Harvey P. Dale, Oct 06 2017 *)

Formula

a(n) = if n<=2 then n else 2^(floor(n/3)+1) + n mod 3 - 1. - Reinhard Zumkeller, Jun 05 2005

G.f.:-x*(1+3*x+6*x^2+7*x^3+6*x^4+4*x^5+2*x^6)/((2*x^3-1)*(x^2+x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]

Extensions

Description corrected by Henrik Lundquist, Jun 06 2005