A171942 Forward van Eck transform of A000120.

0, 1, 2, 2, 4, 1, 3, 4, 8, 1, 2, 2, 5, 1, 5, 8, 16, 1, 2, 2, 4, 1, 3, 4, 9, 1, 2, 2, 7, 1, 9, 16, 32, 1, 2, 2, 4, 1, 3, 4, 8, 1, 2, 2, 5, 1, 5, 8, 17, 1, 2, 2, 4, 1, 3, 4, 11, 1, 2, 2, 11, 1, 17, 32, 64, 1, 2, 2, 4, 1, 3, 4, 8, 1, 2, 2, 5, 1, 5, 8, 16, 1, 2, 2, 4, 1, 3, 4, 9, 1, 2, 2, 7, 1, 9, 16, 33, 1, 2, 2

Offset: 1

Author

N. J. A. Sloane, Oct 25 2010

Keywords

• nonn

Comments

Assumes that the offset of A000120 has been changed to 1.

Comment from Marc LeBrun, Jan 01 2014: A057168(n) - n (the difference between n and the next number with the same binary weight) matches A171942, "Forward van Eck transform of A000120" (the weight of n). Response from M. F. Hasler, Jan 01 2014: The "forward van Eck transform" is the sequence of gaps to the next term with equal value: FVE(a) = n -> min { m>0 | a(n+m)=a(n) } with the (exceptional) convention that : min {} = 0. (See A171898.) So your observation is exactly the definition.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000120, A057168, A171898.

Programs

Haskell

a171942 1 = 0
a171942 n = head [m | m <- [1..], a000120 (m + n - 1) == a000120 (n - 1)]
-- Reinhard Zumkeller, Jan 01 2014

Python

def A171942(n): return (((n-1&~(b:=n-1+(a:=n-1&-n+1)))>>a.bit_length())^b)-n+1 # Chai Wah Wu, Mar 06 2025