A066812 Numbers k such that phi(k+1) = phi(k-1).

5, 8, 9, 11, 27, 33, 71, 75, 123, 147, 309, 315, 387, 513, 555, 573, 627, 636, 729, 795, 843, 911, 915, 1016, 1083, 1227, 1323, 1331, 1347, 1467, 1515, 1609, 1755, 1995, 2133, 2171, 2187, 2307, 2403, 2427, 2475, 2591, 2643, 2696, 2763, 2907, 3243, 3315

Offset: 1

Author

Benoit Cloitre, Jan 20 2002

Keywords

• nonn

Comments

a(n) is even for n = 2,18,24,44,67 while a(n) is odd for other values of n < 85.

a(n) is even for 63 out of the first 10^4 terms. - Amiram Eldar, May 07 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Crossrefs

Cf. A000010 (phi), A001494.

Programs

Mathematica

Flatten[Position[Partition[EulerPhi[Range[3400]],3,1],?(#[[1]]== #[[3]]&), 1,Heads->False]]+1 (* _Harvey P. Dale, Apr 18 2018 *)

PARI

isok(k) = { eulerphi(k+1) == eulerphi(k-1) } \\ Harry J. Smith, Mar 29 2010

Formula

Conjecture: there is a constant 2 < c < 2.1 such that a(n)=n^c asymptotically.

a(n) = A001494(n) + 1.

Extensions

Corrected by Ralf Stephan, Feb 20 2004