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 A080079 Least number causing the longest carry sequence when adding numbers <= n to n in binary representation. 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA From Benoit Cloitre, Feb 22 2003: (Start) a(n) = A004755(n) - 2n. 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(2n) = 2a(n), a(2n+1) = 2a(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 MAPLE # 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A327489, A004755, A062383, A080080, A240769, A006257. Sequence in context: A281589 A302436 A283167 * A318569 A277749 A227629 Adjacent sequences:  A080076 A080077 A080078 * A080080 A080081 A080082 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Jan 26 2003 STATUS approved

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Last modified October 23 20:01 EDT 2019. Contains 328373 sequences. (Running on oeis4.)