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 A255054 Run lengths in A255072. 8
 1, 2, 3, 1, 4, 3, 1, 4, 4, 4, 3, 1, 4, 4, 5, 3, 4, 4, 4, 3, 1, 4, 4, 5, 3, 7, 5, 4, 4, 4, 5, 3, 4, 4, 4, 3, 1, 4, 4, 5, 3, 7, 5, 4, 7, 6, 4, 6, 5, 4, 4, 4, 5, 3, 7, 5, 4, 4, 4, 5, 3, 4, 4, 4, 3, 1, 4, 4, 5, 3, 7, 5, 4, 7, 6, 4, 6, 5, 4, 7, 6, 7, 8, 5, 6, 6, 4, 6, 5, 4, 4, 4, 5, 3, 7, 5, 4, 7, 6, 4, 6, 5, 4, 4, 4, 5, 3, 7, 5, 4, 4, 4, 5, 3, 4, 4, 4, 3, 1, 4, 4, 5, 3, 7, 5, 4, 7, 6, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of integers k which require exactly n steps to reach 0, when starting from k and iterating the map: x -> x - (number of runs in binary representation of x). LINKS Antti Karttunen, Table of n, a(n) for n = 0..16143 FORMULA a(n) = A255053(n+1) - A255053(n). a(n) = 1 + A255055(n) - A255053(n). Other identities. For all n >= 0: a(n) = 1 + A255123(n) + A255124(n). EXAMPLE 0 is the only number reached from 0 in zero steps, thus a(0) = 1. Both 1 and 2, in binary '1' and '10', when the number of runs (A005811) is subtracted from them, result zero: 1-1 = 2-2 = 0, and these are only such numbers where the zero is reached with one step, thus a(1) = 2. For 3, 4 and 5, in binary '11', '100' and '101', subtracting the number of runs results 2 in all cases, thus two steps are requires to reach zero, and as there are no other such cases, a(2) = 3. For 6, in binary '110', subtracting A005811 repeatedly gives -> 6-2 = 4, 4-2 = 2, 2-2 = 0, three steps in total, and as 6 is the only such number requiring three steps, a(3) = 1. PROG (Scheme, with Antti Karttunen's IntSeq-library, three versions): (define (A255054 n) (- (A255053 (1+ n)) (A255053 n))) (define (A255054 n) (+ 1 (- (A255055 n) (A255053 n)))) (define (A255054 n) (+ (A255123 n) (A255124 n) 1)) CROSSREFS Cf. A005811, A236840, A255053, A255055, A255072, A255123, A255124, A255056. Cf. A255059 (positions of odd terms), A255060 (positions of even terms), A255061 (apart from its second term 1, gives positions of ones here). Analogous sequences: A086876, A219644, A219654. Sequence in context: A331791 A365327 A125933 * A011857 A242360 A299927 Adjacent sequences: A255051 A255052 A255053 * A255055 A255056 A255057 KEYWORD nonn AUTHOR Antti Karttunen, Feb 14 2015 STATUS approved

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Last modified August 14 02:49 EDT 2024. Contains 375146 sequences. (Running on oeis4.)