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A217871 a(n)=b(n,1) where b(0,m)=m, b(n,m)=b(floor(n/4),m*2).

%I A217871 #19 Mar 12 2025 18:42:02
%S A217871 1,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%T A217871 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,16,16,16,
%U A217871 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16
%N A217871 a(n)=b(n,1) where b(0,m)=m, b(n,m)=b(floor(n/4),m*2).
%C A217871 Part of the Newton integer square-root finding process. Establishes the upper bound a(n) >= A000196(n) for all n >= 0.
%F A217871 a(n)=b(n,1) where b(0,m)=m; b(n,m)=b(floor(n/4),m*2).
%F A217871 a(n)=2^ceiling(A029837(n+1)/2).
%o A217871 (Common Lisp)
%o A217871 (defun A217871 (n)
%o A217871   (labels ((rec (n guess)
%o A217871            (if (zerop n)
%o A217871                guess
%o A217871                (rec (floor n 4) (* guess 2)))))
%o A217871     (rec n 1))) ;; _James Spahlinger_, Oct 14 2012
%Y A217871 Cf. A000196
%K A217871 nonn
%O A217871 0,2
%A A217871 _James Spahlinger_, Oct 13 2012