A225843 Integral parts of sums of the reciprocals of the Collatz (3x+1) sequence starting with n.

1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset: 1

Author

Reinhard Zumkeller, May 16 2013

Keywords

• nonn

Comments

a(n) = floor(sum(1/A070165(n,k): k = 1..A006577(n)));

conjecture: a(n) <= 3;

a(n) = 1 iff n = 2^k: a(A000079(n)) = 1, a(A057716(n)) > 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Programs

Haskell

a225843 = floor . sum . map (recip . fromIntegral) . a070165_row

Formula

a(n) = floor(A225761(n)/A225784(n)).