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A239356
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Begin with a(0) = 3. Let a(n) for n > 0 be the smallest positive integer not yet in the sequence which forms part of a Primitive Pythagorean Triple (PPT) when paired with a(n-1).
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1
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3, 4, 5, 12, 13, 84, 85, 36, 77, 2964, 2573, 3925, 1116, 637, 1285, 893, 924, 43, 925, 372, 997, 497004, 497005, 138204, 82597, 161005, 39973, 155964, 386827, 417085, 258037, 327684, 139763, 356245, 225924, 82643, 240565, 37164, 13573, 39565, 2388, 39637, 26412, 11515, 28813
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OFFSET
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0,1
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COMMENTS
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I.e., the GCD of a(n) and a(n-1) is 1. That is why a(4)= 13 as opposed to A235598(4), which is 9.
Is the sequence infinite? Probably. But will it eventually contain all the terms of A042965 which are greater than 2? Probably not.
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LINKS
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MATHEMATICA
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f[s_List] := Block[{n = s[[-1]]}, sol = Solve[ x^2 + y^2 == z^2 && GCD[x, y, z] == 1 && x > 0 && y > 0 && z > 0 && (x == n || z == n), {x, y, z}, Integers]; Append[s, Min[ Complement[ Union[ Extract[ sol, Position[ sol, _Integer]]], s]]]]; lst = Nest[f, {3}, 25]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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