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

1,1

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)

Mathematica

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

Crossrefs

Cf. A112322.

Sequence in context: A034378 A062387 A029784 * A059931 A027382 A164840

Adjacent sequences: A112732 A112733 A112734 * A112736 A112737 A112738

Keyword

nonn,base,fini,full

Author

Lekraj Beedassy, Sep 16 2005

Extensions

Corrected and extended by Don Reble, Nov 22 2006

Status

approved