Monica Set
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A018252, A102218, and A102219 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
25-11-2020
1391
Monica Set
The 
th Monica set 
is defined as the set of composite numbers 
for which ![n|[S(x)-S_p(x)]](https://mathworld.wolfram.com/images/equations/MonicaSet/Inline4.gif)
, where
and
Every Monica set has an infinite number of elements.
The Monica set 
is a superset of the Suzanne set 
.
The following table gives the first few Monica numbers in 
for small 
.
 |
OEIS |
 |
| 1 |
A018252 |
1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ... |
| 2 |
A102218 |
4, 8, 10, 12, 14, 15, 22, 26, 27, 35, 42, 44, ... |
| 3 |
A102219 |
9, 16, 24, 27, 28, 32, 40, 42, 49, 52, 56, 60, ... |
If 
is a Smith number, then it is a member of the Monica set 
for all 
. For any integer 
, if 
is a 
-Smith number, then 
.
REFERENCES:
Sloane, N. J. A. Sequences A018252, A102218, and A102219 in "The On-Line Encyclopedia of Integer Sequences."
Smith, M. "Cousins of Smith Numbers: Monica and Suzanne Sets." Fib. Quart. 34, 102-104, 1996.
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