cp's OEIS Frontend

A036571 Binary packing of Connell sequence (shifted once right).

%I A036571 #10 Jul 27 2022 02:41:43
%S A036571 0,1,3,11,27,91,347,859,2907,11099,43867,109403,371547,1420123,
%T A036571 5614427,22391643,55946075,190163803,727034715,2874518363,11464452955,
%U A036571 45824191323,114543668059,389421575003
%N A036571 Binary packing of Connell sequence (shifted once right).
%C A036571 Binary representation of n has 1's at positions specified by Connell sequence (A001614).
%F A036571 a(0)=0, a(n) = a(n-1) + 2^((2*n - floor((1/2)*(1 + sqrt(8*n - 7)))) - 1).
%e A036571 347=101011011 in binary, with 1's at positions 1,2,4,5,7,9.
%o A036571 (Python)
%o A036571 from itertools import count, islice
%o A036571 from math import isqrt
%o A036571 def A036571_gen(): # generator of terms
%o A036571     c = 0
%o A036571     for n in count(1):
%o A036571         yield c
%o A036571         c += 1<<(m:=n<<1)-(k:=isqrt(m))-int((m<<2)>(k<<2)*(k+1)+1)-1
%o A036571 A036571_list = list(islice(A036571_gen(),25)) # _Chai Wah Wu_, Jul 26 2022
%Y A036571 Cf. A001614, A048721, A048722.
%K A036571 nonn
%O A036571 0,3
%A A036571 _Antti Karttunen_