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Binary packing of Connell sequence (shifted once right).
2

%I #10 Jul 27 2022 02:41:43

%S 0,1,3,11,27,91,347,859,2907,11099,43867,109403,371547,1420123,

%T 5614427,22391643,55946075,190163803,727034715,2874518363,11464452955,

%U 45824191323,114543668059,389421575003

%N Binary packing of Connell sequence (shifted once right).

%C Binary representation of n has 1's at positions specified by Connell sequence (A001614).

%F a(0)=0, a(n) = a(n-1) + 2^((2*n - floor((1/2)*(1 + sqrt(8*n - 7)))) - 1).

%e 347=101011011 in binary, with 1's at positions 1,2,4,5,7,9.

%o (Python)

%o from itertools import count, islice

%o from math import isqrt

%o def A036571_gen(): # generator of terms

%o c = 0

%o for n in count(1):

%o yield c

%o c += 1<<(m:=n<<1)-(k:=isqrt(m))-int((m<<2)>(k<<2)*(k+1)+1)-1

%o A036571_list = list(islice(A036571_gen(),25)) # _Chai Wah Wu_, Jul 26 2022

%Y Cf. A001614, A048721, A048722.

%K nonn

%O 0,3

%A _Antti Karttunen_