OFFSET
1,1
COMMENTS
It would be nice to remove the word "Conjectured" from the description. - N. J. A. Sloane
The values of a(3), a(15) and a(21) listed above, namely 0, are conjectural. There is no natural number k < 10^6 satisfying the "homomorphic condition" phi(n+k) = phi(n) + phi(k) for n = 3, 15, 21.
The terms for which there is no solution k < 10^6 are n = 3, 15, 21, 39, 45, 57, 69, 105, 147, 165, 177, 195, 213, 273, 285,..., which satisfy n=3 (mod 6). - T. D. Noe, Jan 20 2004
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, 3rd Ed., New York, Springer-Verlag, 2004, Section B36.
MATHEMATICA
a[ n_ ] := Min[ Select[ Range[ 1, 10^6 ], EulerPhi[ 1, n + # ] == EulerPhi[ 1, n ] + EulerPhi[ 1, # ] & ] ]; Table[ a[ i ], {i, 1, 21} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Dec 27 2001
EXTENSIONS
More terms from T. D. Noe, Jan 20 2004
STATUS
approved