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 A119387 a(n) is the number of binary digits (1's and nonleading 0's) which remain unchanged in their positions when n and (n+1) are written in binary. 4
 0, 0, 1, 0, 2, 1, 2, 0, 3, 2, 3, 1, 3, 2, 3, 0, 4, 3, 4, 2, 4, 3, 4, 1, 4, 3, 4, 2, 4, 3, 4, 0, 5, 4, 5, 3, 5, 4, 5, 2, 5, 4, 5, 3, 5, 4, 5, 1, 5, 4, 5, 3, 5, 4, 5, 2, 5, 4, 5, 3, 5, 4, 5, 0, 6, 5, 6, 4, 6, 5, 6, 3, 6, 5, 6, 4, 6, 5, 6, 2, 6, 5, 6, 4, 6, 5, 6, 3, 6, 5, 6, 4, 6, 5, 6, 1, 6, 5, 6, 4, 6, 5, 6, 3, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The largest k for which A220645(n,k) > 0 is k = a(n). That is, a(n) is the largest power of 2 that divides binomial(n,i) for 0 <= i <= n. - T. D. Noe, Dec 18 2012 LINKS T. D. Noe, Table of n, a(n) for n = 0..1023 Lukas Spiegelhofer and Michael Wallner, Divisibility of binomial coefficients by powers of primes, arXiv:1604.07089 [math.NT], 2016. Mentions this sequence. FORMULA a(n) = A048881(n) + A086784(n+1). (A048881(n) is the number of 1's which remain unchanged between binary n and (n+1). A086784(n+1) is the number of nonleading 0's which remain unchanged between binary n and (n+1).) a(A000225(n))=0. - R. J. Mathar, Jul 29 2006 a(n) = -valuation(H(n)*n,2) where H(n) is the n-th harmonic number. - Benoit Cloitre, Oct 13 2013 a(n) = A000523(n) - A007814(n) = floor(log(n)/log(2)) - valuation(n,2). - Benoit Cloitre, Oct 13 2013 Recurrence: a(2n) = floor(log_2(n)) except a(0) = 0, a(2n+1) = a(n). - Ralf Stephan, Oct 16 2013, corrected by Peter J. Taylor, Mar 01 2020 a(n) = floor(log_2(A000265(n+1))). - Laura Monroe, Oct 18 2020 EXAMPLE 9 in binary is 1001. 10 (decimal) is 1010 in binary. 2 binary digits remain unchanged (the leftmost two digits) between 1001 and 1010. So a(9) = 2. MAPLE a:= n-> ilog2(n+1)-padic[ordp](n+1, 2): seq(a(n), n=0..128);  # Alois P. Heinz, Jun 28 2021 MATHEMATICA a = {0}; Table[b = IntegerDigits[n, 2]; If[Length[a] == Length[b], c = 1; While[a[[c]] == b[[c]], c++]; c--, c = 0]; a = b; c, {n, 101}] (* T. D. Noe, Dec 18 2012 *) PROG (C) #include #define NMAX 200 int sameD(int a, int b) { int resul=0 ; while(a>0 && b >0) { if( (a &1) == (b & 1)) resul++ ; a >>= 1 ; b >>= 1 ; } return resul ; } int main(int argc, char*argv[]) { for(int n=0; n>=1;     int m_bits = 0;     while (m>>=1) m_bits++;     return m_bits; } /* Laura Monroe, Oct 18 2020 */ CROSSREFS Cf. A048881, A086784. Cf. A070940. Cf. A000265. Sequence in context: A147786 A275019 A337835 * A335905 A055941 A290537 Adjacent sequences:  A119384 A119385 A119386 * A119388 A119389 A119390 KEYWORD easy,nonn,base AUTHOR Leroy Quet, Jul 26 2006 EXTENSIONS More terms from R. J. Mathar, Jul 29 2006 Edited by Charles R Greathouse IV, Aug 04 2010 STATUS approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)