A050473 Smallest k such that phi(k+n)=2*phi(k).

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

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

Table of n, a(n) for n=1..76.

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. A000010, A007015, A050472.

Cf. A110179 (least k such that phi(n+k)=2*phi(n)).

Sequence in context: A002070 A326376 A106052 * A057593 A117008 A337366

Adjacent sequences: A050470 A050471 A050472 * A050474 A050475 A050476

Keyword

nonn

Author

Jud McCranie, Dec 24 1999

Status

approved