|
|
A050473
|
|
Smallest k such that phi(k+n)=2*phi(k).
|
|
5
|
|
|
2, 1, 1, 2, 1, 4, 3, 4, 3, 5, 5, 8, 26, 7, 5, 8, 9, 12, 5, 10, 7, 8, 46, 16, 5, 13, 9, 14, 7, 25, 21, 13, 9, 17, 7, 24, 62, 19, 11, 20, 76, 28, 13, 16, 15, 23, 17, 32, 21, 25, 17, 26, 52, 36, 11, 28, 13, 26, 13, 45, 74, 28, 17, 26, 13, 39, 33, 31, 21, 32, 13, 48, 39, 37, 25, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Makowski proved that the sequence is well-defined.
It appears that k<=2n, with equality for the n in A110196 only. Computations for n<10^6 appear to show that k<n for all but a finite number of n. - T. D. Noe, Jul 15 2005
|
|
REFERENCES
|
R. K. Guy, Unsolved Problems Number Theory, Sect. B36
|
|
LINKS
|
|
|
EXAMPLE
|
phi(13+26)=24=2*phi(13), so a(13) is 26.
|
|
MATHEMATICA
|
Table[k=1; While[EulerPhi[n+k] != 2*EulerPhi[k], k++ ]; k, {n, 100}] (Noe)
|
|
CROSSREFS
|
Cf. A110179 (least k such that phi(n+k)=2*phi(n)).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|