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Super-d Number


An integer n such that 3n^3 contains three consecutive 3s in its decimal representation is called a super-3 number. The first few super-3 numbers are 261, 462, 471, 481, 558, 753, 1036, ... (OEIS A014569). A. Anderson has shown that all numbers ending in 471, 4710, or 47100 are super-3 (Pickover 1995).

In general, a super-d number is a number n such that dn^d contains d ds in its decimal representation. The following table gives the first few super-d numbers for small d.

dOEISsuper-d numbers
2A03274319, 31, 69, 81, 105, 106, 107, 119, ...
3A014569261, 462, 471, 481, 558, 753, 1036, ...
4A0327441168, 4972, 7423, 7752, 8431, 10267, ...
5A0327454602, 5517, 7539, 12955, 14555, 20137, ...
6A03274627257, 272570, 302693, 323576, ...
7A032747140997, 490996, 1184321, 1259609, ...
8A032748185423, 641519, 1551728, 1854230, ...
9A03274917546133, 32613656, 93568867, ...

The following table gives the first few palindromic super-d numbers for small d.

dOEISpalindromic super-d numbers
2A032750131, 181, 333, 454, 919, 969, 1331, ...
3A0327514554, 6776, 17471, 22322, 22722, 28182, 43434, ...
4A03275283338, 1142411, 1571751, 1587851, 2013102, ...
5A0327533975793, 9799979, 39199193, 41299214, 65455456, ...
6A0327542023202, 374929473, 458353854, 499202994, 749858947, ...

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References

Pickover, C. A. Keys to Infinity. New York: Wiley, p. 7, 1995.Sloane, N. J. A. Sequences A014569, A032743, A032744, A032745, A032746, A032747, A032748, A032749, A032750, A032751, A032752, A032753, A032754, A032755, and A032756 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Super-d Number

Cite this as:

Weisstein, Eric W. "Super-d Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Super-dNumber.html

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