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%I #21 Nov 19 2013 14:13:44
%S 1,6,3,16,9,4,14,8,29,5,2,11,25,12,15,21,37,69,13,27,19,26,10,24,30,
%T 42,39,52,20,34,18,28,81,43,36,31,48,7,56,47,61,33,46,17,23,40,32,49,
%U 60,57,22,45,63,54,67,41,38,44,62,55,126,58,108,76,50,92,35,64
%N The digits of a(n) and a(n+1) together can be reordered to form a square; lexicographically earliest sequence of distinct positive integers with this property.
%C A231880 and A231881 eventually merge: A231881(2539) = 2541; A231880(2540) = 2536; A231881(2540,2541,..) = A231880(2541,2542,..) = 2544,2551,.. _Hans Havermann_, Nov 17 2013
%H Hans Havermann, <a href="/A231881/b231881.txt">Table of n, a(n) for n = 0..10000</a>
%t a[0] = 1; a[n_] := a[n] = Block[{k = 1, idm = IntegerDigits@ a[n - 1], t = a@# & /@ Range[0, n - 1]}, Label[start]; While[ MemberQ[t, k], k++]; While[ Select[ Permutations[ Join[idm, IntegerDigits[ k]]], #[[1]] != 0 && IntegerQ[ Sqrt[ FromDigits[ #]]] &] == {}, k++; Goto[start]]; k]; Array[a, 100, 0] (* _Robert G. Wilson v_, Nov 17 2013 *)
%Y A variant of A228407. Cf. A231880.
%K nonn,base
%O 0,2
%A _N. J. A. Sloane_, Nov 17 2013, based on a posting to the Sequence Fans Mailing List by _Andrew Weimholt_, Nov 12 2013
%E Corrected and extended by _Hans Havermann_, Nov 17 2013