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A080079
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Least number causing the longest carry sequence when adding numbers <= n to n in binary representation.
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21
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1, 2, 1, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47
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OFFSET
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1,2
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COMMENTS
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T(n,k) < T(n,a(n)) = A070940(n) for 1 <= k < a(n) and T(n,k) <= T(n,a(n)) for a(n) <= k <= n, where T is defined as in A080080.
a(n) gives the distance from n to the nearest 2^t > n. - Ctibor O. Zizka, Apr 09 2020
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences related to binary expansion of n
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FORMULA
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From Benoit Cloitre, Feb 22 2003: (Start)
a(n) = A004755(n) - 2*n.
a(n) = -n + 2*2^floor(log(n)/log(2)). (End)
From Ralf Stephan, Jun 02 2003: (Start)
a(n) = n iff n = 2^k, otherwise a(n) = A035327(n-1).
a(n) = A062383(n) - n. (End)
a(0) = 0, a(2*n) = 2*a(n), a(2*n+1) = 2*a(n)-1 + 2*[n==0]. - Ralf Stephan, Jan 04 2004
a(n) = A240769(n,1); A240769(n, a(n)) = 1. - Reinhard Zumkeller, Apr 13 2014
a(n) = n + 1 - A006257(n). - Reinhard Zumkeller, Apr 14 2014
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MAPLE
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# Alois P. Heinz observes in A327489:
A080079 := n -> 1 + Bits:-Nor(n, n):
# Likewise:
A080079 := n -> 1 + Bits:-Nand(n, n):
seq(A080079(n), n=1..81); # Peter Luschny, Sep 23 2019
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MATHEMATICA
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Flatten@Table[Nest[Most[RotateRight[#]] &, Range[n], n - 1], {n, 30}] (* Birkas Gyorgy, Feb 07 2011 *)
Table[FromDigits[(IntegerDigits[n, 2] /. {0 -> 1, 1 -> 0}), 2] +
1, {n, 30}] (* Birkas Gyorgy, Feb 07 2011 *)
Table[BitXor[n, 2^IntegerPart[Log[2, n] + 1] - 1] + 1, {n, 30}] (* Birkas Gyorgy, Feb 07 2011 *)
Table[2 2^Floor[Log[2, n]] - n, {n, 30}] (* Birkas Gyorgy, Feb 07 2011 *)
Flatten@Table[Reverse@Range[2^n], {n, 0, 4}] (* Birkas Gyorgy, Feb 07 2011 *)
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PROG
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(Haskell)
a080079 n = (length $ takeWhile (< a070940 n) (a080080_row n)) + 1
-- Reinhard Zumkeller, Apr 22 2013
(MAGMA) [-n+2*2^Floor(Log(n)/Log(2)): n in [1..80]]; // Vincenzo Librandi, Dec 01 2016
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CROSSREFS
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Cf. A327489, A004755, A062383, A080080, A240769, A006257.
Sequence in context: A281589 A302436 A283167 * A341707 A318569 A336280
Adjacent sequences: A080076 A080077 A080078 * A080080 A080081 A080082
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Jan 26 2003
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STATUS
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approved
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