# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a372289 Showing 1-1 of 1 %I A372289 #19 Apr 27 2024 16:46:27 %S A372289 1,5,3,21,5,13,7,85,9,21,11,53,13,29,15,341,17,37,19,85,21,45,23,213, %T A372289 25,53,27,117,29,61,31,1365,33,69,35,149,37,77,39,341,41,85,43,181,45, %U A372289 93,47,853,49,101,51,213,53,109,55,469,57,117,59,245,61,125,63,5461 %N A372289 a(n) = n*(2^e) + ((4^e)-1)/3, where e is the 2-adic valuation of n. %C A372289 Construction: take the binary expansion of n, and substitute "01" for all trailing 0-bits that follow after its odd part (= A000265(n)). See the examples. %H A372289 Index entries for sequences related to binary expansion of n %F A372289 For n >= 0, a(2n+1) = 2n+1. %e A372289 For n=4, "100" in binary, when we substitute 01's for the two trailing 0's, we obtain 21, "10101" in binary, therefore a(4) = 21. %e A372289 For n=11, "1011" in binary, there are no trailing 0's, and thus no changes, therefore a(11) = 11. %p A372289 a := proc(n) padic[ordp](n, 2): n*2^% + ((2^%)^2 - 1)/3 end: %p A372289 seq(a(n), n = 1..64); # _Peter Luschny_, Apr 27 2024 %t A372289 a[n_]:=n*(2^IntegerExponent[n, 2]) + ((4^IntegerExponent[n, 2]) - 1)/3; Array[a, 75] (* _Stefano Spezia_, Apr 26 2024 *) %o A372289 (PARI) A372289(n) = { my(e=valuation(n,2)); ((n*(2^e)) + (((4^e)-1)/3)); }; %o A372289 (Python) %o A372289 def A372289(n): return (n<<(e:=(~n & n-1).bit_length()))+((1<<(e<<1))-1)//3 # _Chai Wah Wu_, Apr 26 2024 %Y A372289 Cf. A000265, A005408 (odd bisection), A007814, A371094 [= a(3n+1)]. %K A372289 nonn %O A372289 1,2 %A A372289 _Antti Karttunen_ and _Ali Sada_, Apr 26 2024 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE