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A065883 Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal). 11

%I

%S 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,

%T 7,29,30,31,2,33,34,35,9,37,38,39,10,41,42,43,11,45,46,47,3,49,50,51,

%U 13,53,54,55,14,57,58,59,15,61,62,63,1,65,66,67,17,69,70,71,18,73,74,75

%N Remove factors of 4 from n (i.e., write n in base 4, drop final zeros, then rewrite in decimal).

%H Indranil Ghosh, <a href="/A065883/b065883.txt">Table of n, a(n) for n = 1..20000</a> (First 1000 terms from Harry J. Smith)

%F If n mod 4 = 0 then a(n) = a(n/4), otherwise a(n) = n.

%F Multiplicative with a(p^e) = 2^(e (mod 2)) if p = 2 and a(p^e) = p^e if p is an odd prime.

%F a(n) = n/4^A235127(n)

%F a(n) = A214392(n) if n mod 16 != 0. - _Peter Kagey_, Sep 02 2015

%F From _Robert Israel_, Dec 08 2015: (Start)

%F G.f.: x/(1-x)^2 - 3 Sum_{j>=1} x^(4^j)/(1-x^(4^j))^2.

%F G.f. satisfies G(x) = G(x^4) + x/(1-x)^2 - 4 x^4/(1-x^4)^2. (End)

%e 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.

%p A065883:= n -> n/4^floor(padic:-ordp(n,2)/2):

%p map(A065883, [$1..1000]); # _Robert Israel_, Dec 08 2015

%t If[Divisible[#,4],#/4^IntegerExponent[#,4],#]&/@Range[80] (* _Harvey P. Dale_, Aug 31 2013 *)

%o (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) }

%o { 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

%o (PARI) a(n)=n/4^valuation(n,4); \\ _Joerg Arndt_, Dec 09 2015

%Y For 2 this produces A000265, for 3 A038502 and for 10 (if n<=100) A065881.

%Y Cf. A214392.

%K base,nonn,mult

%O 1,2

%A _Henry Bottomley_, Nov 26 2001

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)