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A256406 Numbers n such that for some m, A166133(m)=n, A166133(m+1)=n^2-1, in order of increasing m.

%I A256406 #31 Jul 09 2025 04:39:33
%S A256406 3,198,270,570,522,600,822,882,1062,2130,1950,2592,2268,2310,3168,
%T A256406 2970,5502,6702,5022,7350,10038,10428,10500,9438,14562,14010,15288,
%U A256406 17028,18060,19698,17958,19890,18522,20772,29670,20550,22158,16650
%N A256406 Numbers n such that for some m, A166133(m)=n, A166133(m+1)=n^2-1, in order of increasing m.
%C A256406 In other words, the next term in A166133 after n is as large as it can be. Terms are listed in order of appearance in A166133.
%C A256406 With the exception of the initial 3, the terms appear to be a (permuted) subset of A014574; i.e. the divisors of a(n)^2-1 are 1, a(n)-1, a(n)+1, and a(n)^2-1. - _Hans Havermann_, Apr 03 2015
%C A256406 See the "blog" file in A166133 for discussion.
%H A256406 Hans Havermann and John Mason, <a href="/A256406/b256406.txt">Table of n, a(n) for n = 1..6575</a>  [Terms 1 through 480 were computed by Hans Havermann; terms 481 through 6575 by John Mason, Apr 05 2015]
%o A256406 (Haskell)
%o A256406 a256406 n = a256406_list !! (n-1)
%o A256406 a256406_list = f a166133_list where
%o A256406    f (u:vs'@(v:ws)) | u > v || v /= u ^ 2 - 1 = f vs'
%o A256406                     | otherwise               = u : f ws
%o A256406 -- _Reinhard Zumkeller_, Apr 01 2015
%Y A256406 Cf. A014574, A166133, A256407 (sorted version).
%K A256406 nonn
%O A256406 1,1
%A A256406 _N. J. A. Sloane_, Apr 01 2015, based on a comment of _Franklin T. Adams-Watters_ in A166133