The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A120738 a(n) = 4*n - A000120(n). 8
 0, 3, 7, 10, 15, 18, 22, 25, 31, 34, 38, 41, 46, 49, 53, 56, 63, 66, 70, 73, 78, 81, 85, 88, 94, 97, 101, 104, 109, 112, 116, 119, 127, 130, 134, 137, 142, 145, 149, 152, 158, 161, 165, 168, 173, 176, 180, 183, 190, 193, 197, 200, 205, 208, 212, 215, 221, 224, 228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of A090739. a(n) is also the increasing sequence of exponents of x in Product_{k > 1} (1 + x^(2^k - 1)). - Paul Pearson (ppearson(AT)rochester.edu), Aug 06 2008 Related to partial sums of the Ruler sequence A001511 by a(n) = A005187(2n), therefore {a(n)+1} are the indices of 1's in A252488. - M. F. Hasler, Jan 22 2015 LINKS Keith Johnson, and Kira Scheibelhut, Rational Polynomials That Take Integer Values at the Fibonacci Numbers, American Mathematical Monthly 123.4 (2016): 338-346. See p. 340. FORMULA a(n) = log2(16^n/A001316(n)). [This was the original definition.] a(n) = 2n + A005187(n). a(n) = 3n + A011371(n). a(n) = 4n - log2(A001316(n)). a(n) = log2(A061549(n)). 2^a(n) = 16^n/A001316(n) = A061549(n). a(n) = A086343(n) + A001511(n) for n>0. - Alford Arnold, Mar 23 2009 2^a(n) = abs(A067624(n)/A117972(n)). - Johannes W. Meijer, Jul 06 2009 a(n) = Sum_{k>=0} (A030308(n,k)*A000225(k+2)). - Philippe Deléham, Oct 16 2011 a(n) = A005187(2n). - M. F. Hasler, Jan 22 2015 MAPLE a:=n->simplify(log[2](16^n/(add(modp(binomial(n, k), 2), k=0..n)))); a:=n->simplify(log[2](16^n/(2^(n-(padic[ordp](n!, 2)))))); # Note: n-(padic[ordp](n!, 2)) is the number of 1's in the binary expansion of n. - Paul Pearson (ppearson(AT)rochester.edu), Aug 06 2008 MATHEMATICA Table[4 n - DigitCount[n, 2, 1], {n, 0, 58}] (* Michael De Vlieger, Nov 06 2016 *) PROG (PARI) {a(n) = if( n < 0, 0, 4*n - subst( Pol( binary( n ) ), x, 1) ) } /* Michael Somos, Aug 28 2007 */ (PARI) a(n) = 4*n - hammingweight(n); \\ Michel Marcus, Nov 06 2016 (Sage) A120738 = lambda n: 4*n - sum(n.digits(2)) print([A120738(n) for n in (0..58)]) # Peter Luschny, Nov 06 2016 CROSSREFS Cf. A000120, A005187, A086343, A090739, A252488. Sequence in context: A043722 A288175 A214066 * A190306 A189530 A292662 Adjacent sequences:  A120735 A120736 A120737 * A120739 A120740 A120741 KEYWORD easy,nonn AUTHOR Paul Barry, Jun 29 2006 EXTENSIONS Definition simplified by M. F. Hasler, Dec 29 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 17:04 EDT 2020. Contains 337265 sequences. (Running on oeis4.)