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A076967 a(1) = 1, a(n+1) is the smallest square greater than the n-th partial sum. 2

%I

%S 1,4,9,16,36,81,169,324,676,1369,2704,5476,11025,21904,44100,88209,

%T 176400,352836,705600,1411344,2822400,5645376,11296321,22591009,

%U 45185284,90364036,180741136,361494169,722964544,1445976676,2891965729

%N a(1) = 1, a(n+1) is the smallest square greater than the n-th partial sum.

%C Lim_{n->infinity} a(n)/(2^n) = 1.34669079829214755988545564864530863502076381405786.... - _Jon E. Schoenfield_, Oct 04 2013

%H Nathaniel Johnston, <a href="/A076967/b076967.txt">Table of n, a(n) for n = 1..1000</a>

%F Lim_{n->infinity} a(n+1)/a(n) = 2. - _Zak Seidov_, May 03 2009

%e a(5) = 36 because it is the smallest square greater than the sum of a(1)..a(4) = 30.

%p a[1] := 1:a[2] := 4:for n from 3 to 45 do a[n] := ceil(evalf(sqrt(sum(a[i],i=1..n-1)+1/10^19),100))^2; od:seq(a[k],k=1..45);

%t nxt[{p_,a_}]:=Module[{k=1},While[!IntegerQ[Sqrt[p+k]],k++];{2p+k,p+k}]; NestList[nxt,{1,1},30][[All,2]] (* _Harvey P. Dale_, May 30 2020 *)

%Y Cf. A076968.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Oct 21 2002

%E Corrected and extended by _Sascha Kurz_, Jan 22 2003

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Last modified April 21 10:07 EDT 2021. Contains 343148 sequences. (Running on oeis4.)