A030530 n appears A070939(n) times.

0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21

Offset: 0

Author

J. Lowell

Keywords

• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A030190, A053738, A070939, A083651, A083652.

Programs

Haskell

import Data.List (unfoldr)
a030530 n = a030530_list !! (n-1)
a030530_list = 0 : concatMap (\n -> unfoldr
   (\x -> if x == 0 then Nothing else Just (n, div x 2)) n) [1..]
-- Reinhard Zumkeller, Dec 05 2011

Mathematica

Join[{0},Table[Table[n,IntegerLength[n,2]],{n,30}]]//Flatten (* Harvey P. Dale, Oct 20 2016 *)

Formula

A030190(n) = T(a(n), A083652(a(n))-n-1), T as defined in A083651.

a(A083652(k)) = k+1.

Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=1} (-1)^(n+1)/A053738(n) = 0.90457767... . - Amiram Eldar, Feb 18 2024