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 A229134 Square numbers that are the sum of two non-consecutive triangular numbers. 2
 16, 36, 81, 121, 196, 225, 256, 289, 361, 441, 484, 529, 576, 625, 676, 841, 900, 961, 1024, 1156, 1225, 1296, 1444, 1521, 1600, 1681, 1849, 1936, 2116, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3136, 3249, 3481, 3721, 4096, 4356, 4624, 4761, 4900, 5041, 5184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is well known that tri(n) + tri(n+1) is always a square. Sequence includes all terms of A001110 > 1. A number m is a term if and only if there exists k > 1 such that m >= tri(k) and 4m - k^2 + 1 is a perfect square. - Chai Wah Wu, Feb 25 2016 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 EXAMPLE 16 = 15+1, 81 = 78+3 = 66+15. MATHEMATICA nn = 10000; mx = Floor[Sqrt[1 + 8 nn]/2]; tri = Table[n (n + 1)/2, {n, mx}]; t = {}; Do[s = tri[[i]] + tri[[j]]; If[s <= nn && IntegerQ[Sqrt[s]], AppendTo[t, s]], {i, mx - 2}, {j, i + 2, mx}]; t = Union[t] (* T. D. Noe, Sep 17 2013 *) PROG (JavaScript) function isSquare(n) { if (Math.sqrt(n)==Math.floor(Math.sqrt(n))) return true; else return false; } a=new Array(); ac=0; for (i=0; i<100; i++) for (j=i+2; j<100; j++) if (isSquare(i*(i+1)/2+j*(j+1)/2)) a[ac++]=i*(i+1)/2+j*(j+1)/2; a.sort(function(a, b) {return a-b; }); a=trimArray(a); function trimArray(arr) { var j, c=new Array(), i; for (j=0; j= m2 + m: if is_square(j-m2): A229134_list.append(i**2) break m2 += 2*m+1 m += 1 # Chai Wah Wu, Feb 25 2016 CROSSREFS Cf. A000217, A001110. Sequence in context: A050775 A022040 A074985 * A069262 A076956 A075369 Adjacent sequences: A229131 A229132 A229133 * A229135 A229136 A229137 KEYWORD nonn AUTHOR Jon Perry, Sep 15 2013 EXTENSIONS Corrected and extended by T. D. Noe, Sep 17 2013 a(2) = 36 reinserted by Chai Wah Wu, Feb 27 2016 STATUS approved

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Last modified August 10 22:34 EDT 2024. Contains 375058 sequences. (Running on oeis4.)