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 A053187 Nearest square. 12
 0, 1, 1, 4, 4, 4, 4, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Apart from 0, k^2 appears 2k times from a(k^2-k+1) through to a(k^2+k) inclusive. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) = ceil((-1+sqrt(4*n+1))/2)^2. - Robert Israel, Aug 01 2014 G.f.: (1/(1-x))*Sum_{n=0..infinity} (2*n+1)*x^(n^2+n+1)). - Robert Israel, Aug 01 2014.  This is related to the Jacobi theta-function theta'_1(q), see A002483 and A245552. G.f.: x / (1-x) * Sum_{k>0} (2*k - 1) * x^(k^2 - k). - Michael Somos, Jan 05 2015 a(n) = floor(sqrt(n)+1/2)^2. - Mikael Aaltonen, Jan 17 2015 EXAMPLE a(7)=9 since 7 is closer to 9 than to 4. G.f. = x + x^2 + 4*x^3 + 4*x^4 + 4*x^5 + 4*x^6 + 9*x^7 + 9*x^8 + 9*x^9 + ... MAPLE seq(ceil((-1+sqrt(4*n+1))/2)^2, n=0..20); # Robert Israel, Jan 05 2015 MATHEMATICA nearestSq[n_] := Block[{a = Floor@ Sqrt@ n}, If[a^2 + a + 1/2 > n, a^2, a^2 + 2 a + 1]; Array[ nearestSq, 75, 0] (* Robert G. Wilson v, Aug 01 2014 *) PROG (Haskell) a053187 n = a053187_list !! n a053187_list = 0 : concatMap (\x -> replicate (2*x) (x ^ 2)) [1..] -- Reinhard Zumkeller, Nov 28 2011 CROSSREFS Cf. A048760, A053188, A002483, A245552. Cf. A061023, A201053 (nearest cube), A000290. Sequence in context: A114555 A124570 A213083 * A013189 A295643 A190718 Adjacent sequences:  A053184 A053185 A053186 * A053188 A053189 A053190 KEYWORD easy,nonn AUTHOR Henry Bottomley, Mar 01 2000 STATUS approved

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Last modified January 18 03:13 EST 2019. Contains 319260 sequences. (Running on oeis4.)