|
%I #44 Apr 14 2023 10:07:19
%S 0,3,6,7,12,15,14,15,24,27,30,31,28,31,30,31,48,51,54,55,60,63,62,63,
%T 56,59,62,63,60,63,62,63,96,99,102,103,108,111,110,111,120,123,126,
%U 127,124,127,126,127,112,115,118,119,124,127,126,127,120,123,126,127,124,127,126
%N a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z.
%C Fibbinary numbers (A003714) give all integers n >= 0 for which a(n) = 3*n.
%C From _Antti Karttunen_, Feb 21 2016: (Start)
%C Fibbinary numbers also give all integers n >= 0 for which a(n) = A048724(n).
%C Note that there are also other multiples of three in the sequence, for example, A163617(99) = 231 ("11100111" in binary) = 3*77, while 77 ("1001101" in binary) is not included in A003714. Note that 99 is "1100011" in binary.
%C (End)
%H Reinhard Zumkeller, <a href="/A163617/b163617.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = -A163618(-n) for all n in ZZ.
%F Conjecture: a(n) = A003188(n) + (6*n + 1 - (-1)^n)/4. - _Velin Yanev_, Dec 17 2016
%e G.f. = 3*x + 6*x^2 + 7*x^3 + 12*x^4 + 15*x^5 + 14*x^6 + 15*x^7 + 24*x^8 + 27*x^9 + ...
%p A163617 := n -> Bits:-Or(2*n, n):
%p seq(A163617(n), n=0..62); # _Peter Luschny_, Sep 23 2019
%t Table[BitOr[n, 2*n], {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%o (PARI) {a(n) = bitor(n, n<<1)};
%o (PARI) {a(n) = if( n==0 || n==-1, n, 2 * a(n \ 2) + (n%2) * (2 + (-1)^(n \ 2)))};
%o (Haskell)
%o import Data.Bits ((.|.), shiftL)
%o a163617 n = n .|. shiftL n 1 :: Integer
%o -- _Reinhard Zumkeller_, Mar 06 2013
%o (Scheme) (define (A163617 n) (A003986bi n (+ n n))) ;; Here A003986bi implements dyadic bitwise-OR operation (see A003986) - _Antti Karttunen_, Feb 21 2016
%o (Julia)
%o using IntegerSequences
%o A163617List(len) = [Bits("OR", n, n<<1) for n in 0:len]
%o println(A163617List(62)) # _Peter Luschny_, Sep 26 2021
%Y Cf. A003986, A048724, A213370, A163618.
%Y Cf. also A269161.
%K nonn
%O 0,2
%A _Michael Somos_, Aug 01 2009
%E Comment about Fibbinary numbers rephrased by _Antti Karttunen_, Feb 21 2016
|
