A076773 2-nadirs of phi: numbers k such that phi(k-2) > phi(k-1) > phi(k) < phi(k+1) < phi(k+2).

315, 525, 735, 1155, 1365, 1575, 1755, 1785, 1815, 1995, 2145, 2415, 2475, 2805, 3045, 3315, 3465, 3885, 4095, 4125, 4305, 4515, 4725, 4935, 5115, 5145, 5355, 5775, 6045, 6195, 6405, 6435, 6615, 6825, 7035, 7095, 7245, 7395, 7455, 7605, 7665, 8085

Offset

1,1

Comments

I call n a "k-nadir" (or nadir of depth k) of the arithmetical function f if n satisfies f(n-k) > ... > f(n-1) > f(n) < f(n+1) < ... < f(n+k).

If just phi(n-1) > phi(n) < phi(n+1) is required for odd n, does this lead to a different sequence? That is, are there consecutive odd numbers in A161962 or consecutive even numbers in A161963? - Jianing Song, Jan 12 2019

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from G. C. Greubel)

Example

phi(313), ..., phi(317) equal 312, 156, 144, 156, 316, respectively, so 315 is a 2-nadir of phi(n).

Mathematica

Select[Range[3, 10^4], EulerPhi[#-2] > EulerPhi[#-1] > EulerPhi[#] < EulerPhi[#+1] < EulerPhi[#+2] &]

Prog

(SageMath) [n for n in (3..9000) if euler_phi(n-2) > euler_phi(n-1) > euler_phi(n) < euler_phi(n+1) < euler_phi(n+2)] # G. C. Greubel, Feb 27 2019
(Magma) eu:=EulerPhi; f:=func<n|eu(n) lt eu(n+1) and eu(n+1) lt eu(n+2)>; f1:= func<n|eu(n) lt eu(n-1) and eu(n-1) lt eu(n-2)>; [k:k in [3..8100]|f(k) and f1(k)]; // Marius A. Burtea, Feb 19 2020

Crossrefs

Cf. A000010, A161962, A161963.

Sequence in context: A349868 A389079 A349937 * A114807 A109130 A284981

Adjacent sequences: A076770 A076771 A076772 * A076774 A076775 A076776

Keyword

nonn

Author

Joseph L. Pe, Nov 14 2002

Status

approved