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 A192645 Monotonic ordering of set S generated by these rules: if x and y are in S and x^2 - y^2 > 0 then x^2 - y^2 is in S, and 1 and 2 are in S. 5
 1, 2, 3, 5, 8, 16, 21, 24, 39, 55, 60, 63, 135, 185, 192, 231, 247, 252, 255, 320, 369, 377, 416, 432, 437, 440, 512, 551, 567, 572, 575, 944, 945, 1080, 1265, 1457, 1496, 1504, 1512, 1517, 1520, 1521, 1889, 2079, 2448, 2449, 2495, 2584, 2631, 2639 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A192476 for a general discussion. Related sequences: A192645: f(x,y) = x^2 - y^2 > 0, start={1,2}; A192647: f(x,y) = x^2 - y^2 > 0, start={1,3}; A192648: f(x,y) = x^2 - y^2 > 0, start={2,3}; A192649: f(x,y) = x^2 - y^2 > 0, start={1,2,4}. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 EXAMPLE 2^2 - 1^2 = 3; 3^2 - 2^2 = 5, 3^2 - 1^2 = 8; 5^2 - 3^2 = 16, 5^2 - 2^2 = 21, 5^2 - 1^2 = 24. Taking the generating procedure in the order just indicated results in the monotonic ordering of the sequence and also suggests a triangular format for the generated terms: 3; 5, 8; 16, 21, 24; 39, 55, 60, 63; 135, 185, 192, 231, 247; ... MATHEMATICA start = {1, 2}; f[x_, y_] := If[MemberQ[Range[1, 5000], x^2 - y^2], x^2 - y^2] b[x_] := Block[{w = x}, Select[Union[ Flatten[AppendTo[w, Table[f[w[[i]], w[[j]]], {i, 1, Length[w]}, {j, 1, i}]]]], # < 5000 &]]; t = FixedPoint[b, start] (* A192645 *) Differences[t] (* A192646 *) CROSSREFS Cf. A192476, A192646 (first differences). Sequence in context: A305370 A192571 A215525 * A050295 A121649 A306622 Adjacent sequences: A192642 A192643 A192644 * A192646 A192647 A192648 KEYWORD nonn AUTHOR Clark Kimberling, Jul 06 2011 STATUS approved

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Last modified August 15 05:43 EDT 2024. Contains 375172 sequences. (Running on oeis4.)