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%I #14 Nov 06 2018 21:17:28
%S 1,2,2,8,2,8,2,32,2,8,2,32,2,8,2,128,2,8,2,32,2,8,2,128,2,8,2,32,2,8,
%T 2,512,2,8,2,32,2,8,2,512,2,8,2,32,2,8,2,2048,2,8,2,32,2,8,2,2048,2,8,
%U 2,32,2,8,2,8192,2,8,2,32,2,8,2,8192,2,8,2,32,2,8,2,32768,2,8,2,32,2,8,2
%N a(0)=1, a(1)=a(2)=2, a(3)=8 and for n >= 4: if n == 0 (mod 4), a(n)=2, if n == 1 (mod 4), a(n)=8, if n == 2 (mod 4), a(n)=2, if n == 3 (mod 8), a(n)=32, if n = 16k + 15, a(n) = 128*4^k, and if n = 16k+7, a(n) = 128*4^(k-1).
%C It seems that this sequence gives the numbers of "2" in the successive sets of 2, which appear in A174353.
%H Antti Karttunen, <a href="/A174354/b174354.txt">Table of n, a(n) for n = 0..16384</a>
%e a(7) = 32 because 7 = 16*(0) + 7 and a(7) = 128*4^(-1).
%e a(8) = 2 because 8 == 0 (mod 4).
%p A174354 := proc(n)
%p if n <= 3 then
%p return op(n+1,[1,2,2,8]) ;
%p end if;
%p if n mod 4 =0 then
%p 2 ;
%p elif n mod 4 =1 then
%p 8 ;
%p elif n mod 4 = 2 then
%p 2
%p elif n mod 8 = 3 then
%p 32
%p elif n mod 16 = 15 then
%p 128*4^((n-15)/16)
%p elif n mod 16 =7 then
%p 128*4^((n-7)/16-1)
%p end if;
%p end proc:
%p seq(A174354(n),n=0..240) ; # _R. J. Mathar_, Feb 29 2016
%t Nest[Append[#1, Which[Mod[#2, 4] == 0, 2, Mod[#2, 4] == 1, 8, Mod[#2, 4] == 2, 2, Mod[#2, 8] == 3, 32, Mod[#2, 16] == 15, 128*4^Quotient[#2, 16], True, 128*4^(Quotient[#2, 16] - 1)]] & @@ {#, Length@ #} &, {1, 2, 2, 8}, 91] (* _Michael De Vlieger_, Nov 06 2018 *)
%o (PARI) A174354(n) = if(n<=1,1+n,if(3==n,8,if(0==((n%4)%2),2,if(1==(n%4),8,if(3==(n%8),32,if(15==(n%16),128*4^((n-15)/16),128*4^((n-7)/16-1))))))); \\ (Adapted from Maple-program) - _Antti Karttunen_, Nov 06 2018
%Y Cf. A174353.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, Mar 17 2010
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