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 A212591 a(n) = smallest value of k for which A020986(k) = n. 3
 0, 1, 2, 5, 8, 9, 10, 21, 32, 33, 34, 37, 40, 41, 42, 85, 128, 129, 130, 133, 136, 137, 138, 149, 160, 161, 162, 165, 168, 169, 170, 341, 512, 513, 514, 517, 520, 521, 522, 533, 544, 545, 546, 549, 552, 553, 554, 597, 640, 641, 642, 645, 648, 649, 650, 661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Brillhart and Morton derive an omega function for the largest values of k. This sequence appears to be given by a similar alpha function. LINKS Michael Day, Table of n, a(n) for n = 1..10000 J. Brillhart and P. Morton, A case study in mathematical research: the Golay-Rudin-Shapiro sequence, Amer. Math. Monthly, 103 (1996) 854-869. FORMULA a(2*n-1) - a(2*n-2) = (2^(2*k+1)+1)/3 and a(2*n) - a(2*n-1) = (2^(2*k+1)+1)/3 with a(0) = a(1) = 0, where n = (2^k)*(2*m-1) for some integers k >= 0 and m > 0. PROG (PARI) alpha(n)={ if(n<2, return(max(0, n-1))); local(nm1=n-1,       mi=m=ceil(nm1/2),       r=floor(log(m)/log(2)), i, fi, alpha=0, a); forstep(i=1, 2*r+1, 2,     mi/=2;     fi=(1+2^i)\3; alpha+=fi*floor(0.5+mi);        ); alpha*=2; if(nm1%2,   \\ adjust for even n    a=factor(2*m)[1, 2]-1; alpha-= (1+2^(1+2*a))\3;   ); return(alpha); } (J) NB. J function on a vector NB. Beware round-off errors on large arguments NB. ok up to ~ 1e8 alphav =: 3 : 0 n   =. <: y if.+/ ntlo=. n > 0 do. n   =. ntlo#n m   =. >.-: n r   =. <.2^.m f   =. <.3%~2+2^2*>:i.>./>:r z   =. 0 mi  =. m for_i. i.#f do.   z   =. z + (i{f) * <.0.5 + mi =. mi%2 end. nzer=. (+/ @: (0=>./\)@:|.)"1 @: #: m ntlo #^:_1 z - (2|n) * <.-:nzer{f else. ntlo end. ) NB. eg    alphav 1 3 5 100 2 8 33 CROSSREFS Cf. A020985, A020991, A020986. Sequence in context: A322916 A062803 A231756 * A153275 A161154 A174438 Adjacent sequences:  A212588 A212589 A212590 * A212592 A212593 A212594 KEYWORD nonn AUTHOR Michael Day, May 22 2012 EXTENSIONS Minor edits by N. J. A. Sloane, Jun 06 2012 Formula section modified following Joerg Arndt's comment Added comments about round-off in J function STATUS approved

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Last modified November 25 14:33 EST 2020. Contains 338624 sequences. (Running on oeis4.)