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# Super-d Number

An integer such that 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- number is a number such that contains s in its decimal representation. The following table gives the first few super- numbers for small .

 OEIS super- 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- numbers for small .

 OEIS palindromic super- 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."

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