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A236840
n minus number of runs in the binary expansion of n: a(n) = n - A005811(n).
21
0, 0, 0, 2, 2, 2, 4, 6, 6, 6, 6, 8, 10, 10, 12, 14, 14, 14, 14, 16, 16, 16, 18, 20, 22, 22, 22, 24, 26, 26, 28, 30, 30, 30, 30, 32, 32, 32, 34, 36, 36, 36, 36, 38, 40, 40, 42, 44, 46, 46, 46, 48, 48, 48, 50, 52, 54, 54, 54, 56, 58, 58, 60, 62, 62, 62, 62, 64, 64, 64
OFFSET
0,4
COMMENTS
All terms are even. Used by the "number-of-runs beanstalk" sequence A255056 and many of its associated sequences.
LINKS
FORMULA
a(n) = n - A005811(n) = n - A000120(A003188(n)).
a(n) = 2*A255070(n).
MAPLE
A236840 := proc(n) local i, b; if n=0 then 0 else b := convert(n, base, 2); select(i -> (b[i-1]<>b[i]), [$2..nops(b)]); n-1-nops(%) fi end: seq(A236840(i), i=0..69); # Peter Luschny, Apr 19 2014
MATHEMATICA
a[n_] := n - Length@ Split[IntegerDigits[n, 2]]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Jul 16 2023 *)
PROG
(Scheme) (define (A236840 n) (- n (A005811 n)))
CROSSREFS
Cf. A091067 (the positions of records), A106836 (run lengths).
Cf. A255070 (terms divided by 2).
Sequence in context: A356692 A361404 A248781 * A182539 A170887 A103265
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Apr 18 2014
STATUS
approved