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.

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A113318 Numbers whose biquadrates (fourth powers) are exclusionary.

Original entry on oeis.org

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

Views

Author

Lekraj Beedassy, Oct 26 2005

Keywords

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 *)

A113952 Largest exclusionary n-th power (or 0 if no such number exists).

Original entry on oeis.org

408540845584, 449103134312, 51050010415041, 0, 606355001344, 60170087060757, 66045000696445844586496, 0, 3570467226624, 743008370688, 16777216, 0, 9012061295995008299689, 0, 1853020188851841, 0, 0, 1162261467, 1099511627776
Offset: 2

Views

Author

Lekraj Beedassy, Nov 09 2005

Keywords

Comments

An exclusionary n-th power m^n is one made up of digits not appearing in the root m which itself consists of distinct digits. For the corresponding root m, see A113951. In principle, no exclusionary n-th power exists for n=1(mod 4)=A016813.

Examples

			a(10)=3570467226624 because it shares no digit in common with its 10th root 18 and no number with distinct digits greater than 18 exhibits such property.

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

Crossrefs

Cf. A112735, A112993, A113317.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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