cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A112321 Least n-digit number whose square is exclusionary, or 0 if no such number exists.

Original entry on oeis.org

2, 17, 157, 1547, 15094, 203879, 0, 0, 0
Offset: 1

Views

Author

Lekraj Beedassy and Klaus Brockhaus, Sep 08 2005

Keywords

Comments

m has an exclusionary square if m consists of distinct digits and m^2 is made up only of digits not appearing in m.
a(10) = 0 since 10-digit numbers either use all digits or at least one digit more than once; a(n) = 0 for n > 10 since numbers with more than 10 digits use at least one digit more than once.

References

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

Crossrefs

Cf. A112322 (corresponding squares), A110815.

A112735 Exclusionary squares.

Original entry on oeis.org

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

Views

Author

Lekraj Beedassy, Sep 16 2005

Keywords

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.

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
Showing 1-2 of 2 results.