A229552 Numbers k such that phi(k) = phi(k+2) - phi(k+1).

1, 3, 5, 9, 15, 21, 35, 39, 45, 99, 135, 231, 255, 855, 1035, 1295, 1539, 1599, 2015, 4335, 6525, 9177, 14399, 16095, 30495, 55385, 61131, 62799, 65535, 72579, 77615, 110175, 152649, 179295, 244965, 299649, 603459, 619695, 686735, 1876725, 2841915, 3058209

Offset: 1

Author

Vincenzo Librandi, Sep 27 2013

Keywords

• nonn

Links

• Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..324 (terms < 10^13, first 100 terms from Donovan Johnson)

Crossrefs

Cf. A092404, A197112, A057000, A000010, A065557.

Programs

Mathematica

Select[Range[10^6], EulerPhi[#] == EulerPhi[# + 2] - EulerPhi[# + 1] &]
Position[Partition[EulerPhi[Range[31*10^5]],3,1],?(#[[3]]-#[[2]] == #[[1]]&),1,Heads->False]//Flatten (* _Harvey P. Dale, Nov 29 2017 *)

Formula

a(n) = A065557(n) - 2. - Amiram Eldar, Dec 09 2022