%I #17 Apr 01 2014 10:35:30

%S 1,22,31,22,11,32,12,11,31,22,11,33,23,21,23,11,22,13,22,11,32,12,12,

%T 31,22,13,11,22,32,12,11,33,23,21,22,11,31,22,11,31,22,11,22,31,22,13,

%U 12,13,11,21,23,12,12,13,22,11,32,12,12,31,22,11,33,13,12,11,33,11,22,12,31,22,12,12,11,31,22,11,22,12

%N Consider the sequence A235598. Recalling that A235598(n) forms part of a Pythagorean triple, a(n) states its relationship to both a(n-1) and a(n+1). 1 denotes the lesser leg, 2 denotes the greater leg and 3 denotes the hypotenuse. The tens place returns its relationship to the side to its left, a(n-1), and the units place its relationship to the side to its right, a(n+1). a(0)=1.

%C Using the data that is available from _Lars Blomberg_, and the nine possible arrangements, (a), of the three sides, here are those counts for the first x terms not including a(0):

%C \x. 10 100 1000 10000 100000 1000000 3000000 aprx percentage.

%C a\

%C 11:. 3. 21. 164. 1502. 13734. 134087. 401166 ~13.3%

%C 12:. 1. 18. 215. 2120. 21457. 208304. 621859 ~20.7%

%C 13:. 0.. 6.. 94.. 921.. 8884.. 86286. 256802. ~8.5%

%C 21:. 0.. 3.. 51.. 550.. 5120.. 51732. 156588. ~5.2%

%C 22:. 3. 22. 207. 2025. 21013. 214855. 646185 ~21.6%

%C 23:. 0.. 5.. 55.. 657.. 6347.. 64480. 194775. ~6.5%

%C 31:. 2. 12.. 95.. 881.. 8697.. 83631. 249413. ~8.3%

%C 32:. 1.. 7.. 51.. 390.. 4219.. 42112. 126410. ~4.2%

%C 33:. 0.. 6.. 68.. 954. 10529. 114513. 346802 ~11.7%

%H Robert G. Wilson v, <a href="/A239431/b239431.txt">Table of n, a(n) for n = 0..10000</a>

%e a(2)=31 because 5 is the hypotenuse in the 3-4-5 Pythagorean triple, a(n-1) is 4 and 5 is the lesser side in the 5-12-13 Pythagorean triple, a(n+1) is 12.

%t lst={ (* the terms from A235598 *) }; g[j_, k_] := Block[{hyp = Sqrt[ j^2 + k^2], lg = Abs@ Sqrt[ j^2 - k^2]}, If[ IntegerQ@ hyp, If[ Min[j, k] == k, 1, 2], If[ Max[j, k] == k, 3, If[lg > k, 1, 2]]]]; f[n_] := Block[{s = Take[lst, {n - 1, n + 1}]}, 10g[ s[[1]], s[[2]] ] + g[ s[[3]], s[[2]] ]]; f[1] = 1; Array[f, 80]

%Y Cf. A235598, A236243, A236244.

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Mar 20 2014