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

0,1

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

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]

Crossrefs

Cf. A235598.

Sequence in context: A191197 A055493 A109350 * A077034 A076601 A242669

Adjacent sequences: A239353 A239354 A239355 * A239357 A239358 A239359

Keyword

nonn

Author

Robert G. Wilson v, Mar 16 2014

Status

approved