A167767 First of 3 or more consecutive integers with equal values of phi(phi(n)).

1, 2, 7, 8, 20, 31, 32, 33, 146, 211, 314, 384, 626, 674, 1754, 2694, 2695, 5186, 11714, 12242, 17329, 17613, 19310, 25544, 35774, 36728, 38018, 40227, 42626, 56834, 65731, 91106, 97724, 110971, 117536, 131071, 131072, 155821, 161734, 164174

Offset

1,2

Comments

Let p2(n) = phi(phi(n)). This list shows numbers n such that p2(n) = p2(n+1) = p2(n+2) = x for some x.

Here phi is Euler's totient function.

Links

Donovan Johnson, Table of n, a(n) for n = 1..500

Formula

{n: A010554(n) = A010554(n+1) = A010554(n+2)}. - R. J. Mathar, Nov 12 2009

Example

p2(1) = p2(2) = p2(3) = 1, p2(7) = p2(8) = p2(9) = 2.

Mathematica

Select[Range[100], EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 1]] && EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 2]] &] (* G. C. Greubel, Jun 23 2016 *)

Prog

(PARI) isok(n) = (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+1))) && (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+2))) \\ Michel Marcus, Jul 12 2013
(Magma) [n: n in [1..2*10^5] | EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 1)) and EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 2))]; // Vincenzo Librandi, Jun 24 2016

Crossrefs

Cf. A167768.

Sequence in context: A015617 A306903 A026579 * A054601 A279847 A291629

Adjacent sequences: A167764 A167765 A167766 * A167768 A167769 A167770

Keyword

nonn

Author

Fred Schneider, Nov 11 2009

Extensions

Edited by N. J. A. Sloane, Nov 12 2009

Extended by R. J. Mathar, Nov 12 2009

Status

approved