A113318 Numbers whose biquadrates (fourth powers) are exclusionary.

2, 3, 4, 7, 8, 9, 24, 27, 28, 32, 42, 52, 53, 58, 59, 67, 89, 93, 203, 258, 284, 324, 329, 832, 843, 2673

Offset: 1

Author

Lekraj Beedassy, Oct 26 2005

Keywords

• base
• nonn
• fini

Comments

The number m with no repeated digits has an exclusionary fourth power m^4 if the latter is made up of digits not appearing in m. Is a subsequence of A111116. Conjectured to be complete. For the corresponding exclusionary biquadrates m^4, see A113317.

References

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

Programs

Mathematica

ebQ[n_]:=Max[DigitCount[n]]==1&&Intersection[IntegerDigits[n], IntegerDigits[ n^4]]=={}; Select[Range[3000],ebQ] (* Harvey P. Dale, Aug 21 2013 *)