A168223 a(n) = A006369(n) - A006368(n).

0, 0, 0, 0, -1, 3, -5, 4, -1, -1, -2, 7, -10, 7, -2, -1, -3, 10, -15, 11, -3, -2, -4, 14, -20, 14, -4, -2, -5, 17, -25, 18, -5, -3, -6, 21, -30, 21, -6, -3, -7, 24, -35, 25, -7, -4, -8, 28, -40, 28, -8, -4, -9, 31, -45, 32, -9, -5, -10, 35, -50, 35, -10, -5, -11, 38, -55, 39

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2009

Keywords

• sign
• easy
• look

Comments

A047342 and A168223 give record values and where they occur: a(A168224(n))=A047342(n) and a(m) < A047342(n) for m < A168224(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for linear recurrences with constant coefficients, signature (-2,-2,0,3,4,3,0,-2,-2,-1).

Programs

Haskell

a168223 n = a006369 n - a006368 n  -- Reinhard Zumkeller, Mar 15 2014

Mathematica

LinearRecurrence[{-2,-2,0,3,4,3,0,-2,-2,-1},{0, 0, 0, 0, -1, 3, -5, 4, -1, -1},50] (* G. C. Greubel, Jul 16 2016 *)

Formula

a(12*n) = -10*n, a(12*n+1) = 7*n.

a(12*n+2) = -2*n, a(12*n+3) = -n.

a(12*n+4) = -2*n - 1, a(12*n+5) = 7*n + 3.

a(12*n+6) = -10*n - 5, a(12*n+7) = 7*n + 4.

a(12*n+8) = -2*n -1, a(12*n+9) = -n - 1.

a(12*n+10) = -2*n - 2, a(12*n+11) = 7*n + 7.

G.f.: -x^4*(x^2-x+1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^2+x+1)^2). - Colin Barker, Apr 04 2013