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 A234334 Numbers k such that both distances from k to two nearest squares are perfect squares. 5
 0, 1, 5, 8, 25, 40, 45, 65, 80, 153, 160, 169, 200, 221, 325, 360, 416, 425, 493, 520, 625, 680, 725, 925, 936, 1025, 1040, 1073, 1088, 1305, 1360, 1681, 1768, 1800, 1813, 1845, 1961, 2000, 2320, 2385, 2501, 2600, 2925, 3016, 3185, 3200, 3400, 3445, 3721, 3848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Except a(1)=0, a(n) are numbers k such that both k-x and y-k are perfect squares, where x and y are two nearest to k squares: x < k <= y. The sequence of sums of distances begins: 1, 1, 5, 5, 9, 13, 13, 17, 17, 25, 25, 25, 29, 29, 37, 37, 41, 41, 45, 45, 49, 53, 53, 61, 61, 65, 65, 65, 65, 73, 73, 81, 85, ... (cf. A057653). Each term is either a square or has a pair: if i^2 + j^2 = 2*m+1 then m^2+i^2 and m^2+j^2 are both in the sequence. LINKS Robert Israel, Table of n, a(n) for n = 1..6000 EXAMPLE The two squares nearest to 25 are 16 and 25, because both 25-25=0 and 25-16=9 are squares, 25 is in the sequence. The two squares nearest to 45 are 36 and 49, because both 45-36=9 and 49-45=4 are squares, 45 is in the sequence. MAPLE filter:= proc(n) local a; if issqr(n) then a:= sqrt(n)-1 else a:= floor(sqrt(n)) fi; issqr(n-a^2) and issqr((a+1)^2-n) end proc: select(filter, [\$0..5000]); # Robert Israel, Jan 21 2021 MATHEMATICA filter[n_] := If[n == 0, True, Module[{a}, a = If[IntegerQ @ Sqrt[n], Sqrt[n]-1, Floor[Sqrt[n]]]; IntegerQ @ Sqrt[n-a^2] && IntegerQ@Sqrt[(a+1)^2-n]]]; Select[Range[0, 5000], filter] (* Jean-François Alcover, May 28 2023, after Robert Israel *) CROSSREFS Cf. A000290. Cf. subsequences: A007204, A234335, A234336. Cf. A234348. Sequence in context: A346552 A166652 A286571 * A025623 A069959 A038250 Adjacent sequences: A234331 A234332 A234333 * A234335 A234336 A234337 KEYWORD nonn,easy,changed AUTHOR Alex Ratushnyak, Dec 23 2013 STATUS approved

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Last modified May 29 07:13 EDT 2023. Contains 363029 sequences. (Running on oeis4.)