A239356 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).

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

Offset: 0

Author

Robert G. Wilson v, Mar 16 2014

Keywords

• nonn

Comments

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.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A235598.

Programs

Mathematica

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]