A226060 First differences of A213709.

0, 1, 1, 2, 4, 8, 13, 24, 44, 81, 151, 284, 536, 1012, 1910, 3606, 6818, 12922, 24561, 46821, 89509, 171580, 329760, 635357, 1227025, 2374558, 4602962, 8933547, 17352195, 33718878, 65534953, 127379679, 247598613, 481334017, 935936312, 1820567772, 3543113588

Offset: 0

Author

Antti Karttunen, Jun 12 2013

Keywords

• nonn

Comments

Also, apart from the first term a(0)=0, the number of terms in A179016 whose binary width is n+2 bits and whose two most significant bits are both ones. For example, there is one term 7 (111) in three-bit range; one term 15 (1111) in four bit range; two such terms, 26 (11010) and 31 (11111) in five-bit range; four terms: 49, 53, 57, 63 in six-bit range and eight terms: 97, 101, 104, 109, 112, 116, 120, 127 in seven-bit range.

For n >= 4, a(n) = number of steps to go from 2^(n+2) to (2^(n+1) + 2^n + 1) using the iterative process described in A071542.

Ratio a(n)/A213709(n) develops as: 0, 1, 0.5, 0.667..., 0.8, 0.889..., 0.765..., 0.8, 0.815..., 0.827..., 0.844..., 0.861..., 0.873..., 0.88..., 0.883..., 0.886..., 0.888..., 0.891..., 0.896..., 0.901..., 0.906..., 0.911..., 0.916..., 0.921..., 0.926..., 0.93..., 0.934..., 0.937..., 0.94..., 0.941..., 0.942..., 0.943..., 0.943..., 0.944..., 0.944..., 0.945..., 0.945..., 0.946..., 0.947..., 0.949..., 0.95..., 0.951..., 0.953..., 0.954..., 0.955..., 0.957..., 0.958...

Links

• Antti Karttunen, Table of n, a(n) for n = 0..46

Crossrefs

Cf. A213709, A071542.

Programs

Scheme

(define (A226060 n) (- (A213709 (+ n 1)) (A213709 n)))

Formula

a(n) = A213709(n+1) - A213709(n).