The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065883 Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal). 15
 1, 2, 3, 1, 5, 6, 7, 2, 9, 10, 11, 3, 13, 14, 15, 1, 17, 18, 19, 5, 21, 22, 23, 6, 25, 26, 27, 7, 29, 30, 31, 2, 33, 34, 35, 9, 37, 38, 39, 10, 41, 42, 43, 11, 45, 46, 47, 3, 49, 50, 51, 13, 53, 54, 55, 14, 57, 58, 59, 15, 61, 62, 63, 1, 65, 66, 67, 17, 69, 70, 71, 18, 73, 74, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 1..20000 (First 1000 terms from Harry J. Smith) FORMULA If n mod 4 = 0 then a(n) = a(n/4), otherwise a(n) = n. Multiplicative with a(p^e) = 2^(e (mod 2)) if p = 2 and a(p^e) = p^e if p is an odd prime. a(n) = n/4^A235127(n). a(n) = A214392(n) if n mod 16 != 0. - Peter Kagey, Sep 02 2015 From Robert Israel, Dec 08 2015: (Start) G.f.: x/(1-x)^2 - 3 Sum_{j>=1} x^(4^j)/(1-x^(4^j))^2. G.f. satisfies G(x) = G(x^4) + x/(1-x)^2 - 4 x^4/(1-x^4)^2. (End) Sum_{k=1..n} a(k) ~ (2/5) * n^2. - Amiram Eldar, Nov 20 2022 EXAMPLE a(7)=7, a(14)=14, a(28)=a(4*7)=7, a(56)=a(4*14)=14, a(112)=a(4^2*7)=7. MAPLE A065883:= n -> n/4^floor(padic:-ordp(n, 2)/2): map(A065883, [\$1..1000]); # Robert Israel, Dec 08 2015 MATHEMATICA If[Divisible[#, 4], #/4^IntegerExponent[#, 4], #]&/@Range[80] (* Harvey P. Dale, Aug 31 2013 *) PROG (PARI) baseA2B(x, a, b)= { local(d, e=0, f=1); while (x>0, d=x%b; x\=b; e+=d*f; f*=a); return(e) } { for (n=1, 1000, if (n%4, a=n, a=baseA2B(n, 10, 4); while (a%10 == 0, a\=10); a=baseA2B(a, 4, 10)); write("b065883.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 03 2009 (PARI) a(n)=n/4^valuation(n, 4); \\ Joerg Arndt, Dec 09 2015 (Python) def A065883(n): return n>>((~n&n-1).bit_length()&-2) # Chai Wah Wu, Jul 09 2022 CROSSREFS Cf. A214392, A235127, A350091 (drop final 2's). Remove other factors: A000265, A038502, A132739, A244414, A242603, A004151. Sequence in context: A083346 A319652 A327938 * A214392 A071975 A350389 Adjacent sequences: A065880 A065881 A065882 * A065884 A065885 A065886 KEYWORD base,easy,nonn,mult AUTHOR Henry Bottomley, Nov 26 2001 STATUS approved

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

Last modified December 5 09:53 EST 2022. Contains 358585 sequences. (Running on oeis4.)