A231881 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.

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, 42, 39, 52, 20, 34, 18, 28, 81, 43, 36, 31, 48, 7, 56, 47, 61, 33, 46, 17, 23, 40, 32, 49, 60, 57, 22, 45, 63, 54, 67, 41, 38, 44, 62, 55, 126, 58, 108, 76, 50, 92, 35, 64

Offset: 0

Author

N. J. A. Sloane, Nov 17 2013, based on a posting to the Sequence Fans Mailing List by Andrew Weimholt, Nov 12 2013

Keywords

• nonn
• base

Comments

A231880 and A231881 eventually merge: A231881(2539) = 2541; A231880(2540) = 2536; A231881(2540,2541,..) = A231880(2541,2542,..) = 2544,2551,.. Hans Havermann, Nov 17 2013

Links

• Hans Havermann, Table of n, a(n) for n = 0..10000

Crossrefs

A variant of A228407. Cf. A231880.

Programs

Mathematica

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 *)

Extensions

Corrected and extended by Hans Havermann, Nov 17 2013