Smarandache Ceil Function
المؤلف:
Sloane, N. J. A
المصدر:
Sequences A000027/M0472, A019554, A019555, and A053166 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
29-11-2020
1068
Smarandache Ceil Function
A Smarandache-like function which is defined where 
is defined as the smallest integer for which 
. The Smarandache 
function can therefore be obtained by replacing any factors which are 
th powers in 
by their 
roots.
where 
is the number of solutions to 
.
The functions 
for 
, 3, ..., 6 for values such that 
are tabulated by Begay (1997). The following table gives 
for small 
and 
, 2, ....
 |
OEIS |
 |
| 1 |
A000027 |
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... |
| 2 |
A019554 |
1, 2, 3, 2, 5, 6, 7, 4, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ... |
| 3 |
A019555 |
1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 4, 17, 6, ... |
| 4 |
A053166 |
1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 6, 13, 14, 15, 2, 17, 6, ... |
REFERENCES:
Begay, A. "Smarandache Ceil Functions." Bull. Pure Appl. Sci. 16E, 227-229, 1997. https://www.gallup.unm.edu/~smarandache/smarceil.htm.
Sloane, N. J. A. Sequences A000027/M0472, A019554, A019555, and A053166 in "The On-Line Encyclopedia of Integer Sequences."
Smarandache, F. Collected Papers, Vol. 2. Kishinev, Moldova: Kishinev University Press, 1997.
Smarandache, F. Only Problems, Not Solutions!, 4th ed. Phoenix, AZ: Xiquan, 1993.
Weisstein, E. W. "Gigantic Primes with Prime Digits Found." MathWorld Headline News, Apr. 9, 2002. https://mathworld.wolfram.com/news/2002-04-09/primeprimes/.
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