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A076967 a(1) = 1, a(n+1) is the smallest square greater than the n-th partial sum. 2
1, 4, 9, 16, 36, 81, 169, 324, 676, 1369, 2704, 5476, 11025, 21904, 44100, 88209, 176400, 352836, 705600, 1411344, 2822400, 5645376, 11296321, 22591009, 45185284, 90364036, 180741136, 361494169, 722964544, 1445976676, 2891965729 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Lim_{n->infinity} a(n)/(2^n) = 1.34669079829214755988545564864530863502076381405786.... - Jon E. Schoenfield, Oct 04 2013

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

FORMULA

Lim_{n->infinity} a(n+1)/a(n) = 2. - Zak Seidov, May 03 2009

EXAMPLE

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

MAPLE

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);

MATHEMATICA

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 *)

CROSSREFS

Cf. A076968.

Sequence in context: A018228 A204503 A138858 * A233247 A231180 A250029

Adjacent sequences:  A076964 A076965 A076966 * A076968 A076969 A076970

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Oct 21 2002

EXTENSIONS

Corrected and extended by Sascha Kurz, Jan 22 2003

STATUS

approved

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)