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.
d OEIS super-d numbers
2 A032743 19,
31, 69, 81, 105, 106, 107, 119, ...
3 A014569 261,
462, 471, 481, 558, 753, 1036, ...
4 A032744 1168,
4972, 7423, 7752, 8431, 10267, ...
5 A032745 4602,
5517, 7539, 12955, 14555, 20137, ...
6 A032746 27257,
272570, 302693, 323576, ...
7 A032747 140997, 490996, 1184321,
1259609, ...
8 A032748 185423, 641519, 1551728, 1854230, ...
9 A032749 17546133,
32613656, 93568867, ...
The following table gives the first few palindromic super-d numbers for small d.
d OEIS palindromic
super-d
numbers
2 A032750 131, 181, 333, 454, 919, 969, 1331, ...
3 A032751 4554,
6776, 17471, 22322, 22722, 28182, 43434, ...
4 A032752 83338,
1142411, 1571751, 1587851, 2013102, ...
5 A032753 3975793,
9799979, 39199193, 41299214, 65455456, ...
6 A032754 2023202,
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 NumberCite this as:
Weisstein, Eric W. "Super-d Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Super-dNumber.html