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A255069 First differences of A255071. 2
1, 1, 2, 4, 7, 13, 24, 44, 81, 150, 280, 526, 992, 1875, 3551, 6740, 12823, 24450, 46709, 89383, 171325, 328962, 632849, 1219909, 2356217, 4559224, 8835610, 17144046, 33295497, 64705083, 125802338, 244673791, 476011284, 926373373, 1803512210, 3512774806 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also, a(n) = the number of times a number whose binary expansion begins with 10... (cf. A004754) is encountered when iterating from 2^(n+2)-2 to (2^(n+1))-2 with the map x -> x - (number of runs in binary representation of x), i.e., with m(n) = A236840(n). For example, when starting from the initial value (2^(4+2))-2 = 62, we get m(62) = 60, m(60) = 58, m(58) = 54, m(54) = 50, m(50) = 46, m(46) = 42, m(42) = 36 and finally m(36) = 32, which is (2^(4+1)). Of the nine numbers encountered, only 46, 42, 36 and 32 (in binary: 101110, 101010, 100100 and 100000) are in A004754, thus a(4) = 5.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

a(n) = A255071(n+1) - A255071(n).

For n > 1, a(n-1) = Sum_{k = A255062(n) .. A255061(n+1)}(1-secondmsb(A255056(k))).

Here secondmsb is implemented by the starting offset 2 version of A079944, and effectively gives the second most significant bit in the binary expansion of n. The formula follows from the semi-regular nature of number-of-runs beanstalk, see comments above and at A255071.

PROG

(Scheme)

(define (A255069 n) (- (A255071 (+ n 1)) (A255071 n)))

(define (A255069shifted n) (add (lambda (n) (- 1 (A079944off2 (A255066 n)))) (A255062 n) (A255061 (+ 1 n)))) ;; Cf. A079444.

CROSSREFS

First differences of A255071.

Cf. A004754, A005811, A236840, A255061, A255062, A255056, A255066.

Cf. also A255063, A255064, A255125, A255126.

Analogous sequence: A226060.

Sequence in context: A054175 A305442 A000073 * A160254 A276661 A005318

Adjacent sequences:  A255066 A255067 A255068 * A255070 A255071 A255072

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 21 2015

STATUS

approved

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Last modified November 12 07:03 EST 2019. Contains 329052 sequences. (Running on oeis4.)