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

1,3

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

Formula

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

Prog

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

Crossrefs

Sequence in context: A023588 A175242 A355770 * A327657 A301957 A318874

Adjacent sequences: A225840 A225841 A225842 * A225844 A225845 A225846

Keyword

nonn

Author

Reinhard Zumkeller, May 16 2013

Status

approved