A112735 Exclusionary squares.

4, 9, 16, 49, 64, 81, 289, 324, 576, 841, 1156, 1444, 1521, 2209, 2809, 2916, 3249, 3364, 3481, 3844, 4489, 5184, 6241, 7056, 8464, 8836, 24649, 24964, 29929, 34969, 36864, 37636, 43681, 56169, 56644, 61009, 64009, 66049, 67081, 94249, 98596

Offset: 1

Author

Lekraj Beedassy, Sep 16 2005

Keywords

• nonn
• base
• fini
• full

Comments

An exclusionary square m^2 is one sharing no digit in common with its root m made up of distinct digits. The associated root is given by A112736.

The largest term is 639172^2 = 408540845584; and is the seq. because the intersection of {1,2,3,6,7,9} & {0, 4, 5, 8} = {}. Number of terms < 10^n: 2, 6, 10, 26, 41, 71, 84, 121, 129, 140, 141, 142. - Robert G. Wilson v, Apr 03 2009

References

• H. Ibstedt, Solution to Problem 2623, "Exclusionary Powers", pp. 346-9, Journal of recreational Mathematics, Vol. 32 No. 4 2003-4 Baywood NY.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..142 (full sequence)

Crossrefs

Cf. A112322.

Programs

Mathematica

fQ[n_] := Intersection[ IntegerDigits[n], IntegerDigits[n^2]] == {}; Select[ Range@ 330, fQ@# &]^2 (* Robert G. Wilson v, Apr 03 2009 *)

Extensions

Corrected and extended by Don Reble, Nov 22 2006