A227190 a(n) = n minus (product of run lengths in binary representation of n).

0, 1, 1, 2, 4, 4, 4, 5, 7, 9, 9, 8, 11, 11, 11, 12, 14, 16, 15, 18, 20, 20, 20, 18, 21, 24, 23, 22, 26, 26, 26, 27, 29, 31, 29, 32, 35, 34, 33, 37, 39, 41, 41, 40, 43, 43, 43, 40, 43, 46, 43, 48, 51, 50, 49, 47, 51, 55, 53, 52, 57, 57, 57, 58, 60, 62, 59, 62

Offset: 1

Author

Antti Karttunen, Jul 04 2013

Keywords

• nonn
• base

Examples

			For 8, "1000" in binary, the run lengths are 1 and 3, 1*3=3, and 8-3 = 5, thus a(8)=5. For 24, "11000" in binary, the run lengths are 2 and 3, 2*3=6, and 24-6 = 18, thus a(24)=18.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096

Crossrefs

Cf. A227191, A000975, A084639.

Programs

Haskell

a227190 n = n - a167489 n  -- Reinhard Zumkeller, Jul 05 2013

Mathematica

Table[n-Times@@(Length/@Split[IntegerDigits[n,2]]),{n,70}] (* Harvey P. Dale, Aug 02 2013 *)

Scheme

(define (A227190 n) (- n (A167489 n))) ;; The Scheme-program for A167489 is found under that entry.

Formula

a(n) = n - A167489(n).