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, ...

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."