A113317 Exclusionary biquadrates (fourth powers).

16, 81, 256, 2401, 4096, 6561, 331776, 531441, 614656, 1048576, 3111696, 7311616, 7890481, 11316496, 12117361, 20151121, 62742241, 74805201, 1698181681, 4430766096, 6505390336, 11019960576, 11716114081, 479174066176, 505022001201, 51050010415041

Offset

1,1

Comments

An exclusionary biquadrate m^4 is one sharing no digit in common with its root m made up of distinct digits.

References

Shyam Sunder Gupta, "Exploring the Beauty of Fascinating Numbers", Springer, pp. 43-44.

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

Links

Table of n, a(n) for n=1..26.

Patrick De Geest, Reference table for squares, cubes and biquadrates

Formula

a(n) = A113318(n)^4.

Example

331776 = 24^4 is in the sequence as 331776 and 24 have no digits in common and 24 has distinct digits. - David A. Corneth, May 12 2025

Crossrefs

Subsequence of A000583. Subsequence of A113316.

Roots are given by A113318.

Sequence in context: A050463 A075578 A113316 * A187457 A056118 A372998

Adjacent sequences: A113314 A113315 A113316 * A113318 A113319 A113320

Keyword

base,nonn,fini

Author

Lekraj Beedassy, Oct 26 2005

Extensions

Corrected by Don Reble, Nov 22 2006

a(25)-a(26) added by Patrick De Geest, May 12 2025

a(16) corrected by Falk Hüffner, May 25 2026

Status

approved