An Integer such that contains three consecutive 3s in its Decimal representation. The first few super-3 numbers are 261, 462, 471, 481, 558, 753, 1036, ... (Sloane's A014569). A. Anderson has conjectured that all numbers ending in 471, 4710, or 47100 are super-3 (Pickover 1995).

For a digit , super-3 numbers can be generalized to super- numbers such that contains s in its Decimal representation. The following table gives the first few super- numbers for small .

Sloane | Super- numbers | |

2 | Sloane's A032743 | 19, 31, 69, 81, 105, 106, 107, 119, 127, ... |

3 | Sloane's A014569 | 261, 462, 471, 481, 558, 753, 1036, 1046, ... |

4 | Sloane's A032744 | 1168, 4972, 7423, 7752, 8431, 10267, 11317, ... |

5 | Sloane's A032745 | 4602, 5517, 7539, 12955, 14555, 20137, 20379, ... |

6 | Sloane's A032746 | 27257, 272570, 302693, 323576, 364509, 502785, ... |

7 | Sloane's A032747 | 140997, 490996, 1184321, 1259609, 1409970, ... |

8 | Sloane's A032748 | 185423, 641519, 1551728, 1854230, 6415190, ... |

9 | Sloane's A032749 | 17546133, 32613656, 93568867, 107225764, ... |

**References**

Pickover, C. A. *Keys to Infinity.* New York: Wiley, p. 7, 1995.

Sloane, N. J. A. Sequence A014569 in ``The On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.

© 1996-9

1999-05-26