A143973 Distances between multiples of 3 in A000010.

2, 4, 1, 4, 1, 2, 5, 1, 1, 3, 4, 1, 1, 1, 1, 3, 1, 2, 4, 3, 2, 2, 1, 4, 1, 1, 2, 2, 3, 2, 1, 1, 2, 1, 1, 1, 2, 3, 2, 4, 1, 2, 2, 2, 1, 1, 4, 1, 1, 3, 1, 2, 1, 2, 3, 2, 3, 2, 2, 1, 2, 1, 3, 1, 1, 4, 1, 3, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 2, 1

Offset: 1

Author

J. Perry (johnandruth(AT)jrperry.orangehome.co.uk), Sep 06 2008

Keywords

• nonn

Comments

Inspired by the question: is n == 1 mod phi(n) for n composite?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A008585, A066498.

Programs

Mathematica

Differences @ Position[EulerPhi[Range[200]], ?(Divisible[#, 3] &)] // Flatten (* _Amiram Eldar, Feb 29 2020 *)

Formula

a(1) = 2 since the first two numbers k such that 3 | phi(k) are 7 and 9, and 9 - 7 = 2.

Extensions

Offset corrected and more terms added by Amiram Eldar, Feb 29 2020