Super-d Number
المؤلف:
Pickover, C. A.
المصدر:
Keys to Infinity. New York: Wiley
الجزء والصفحة:
...
19-11-2020
1304
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."
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