A320391 Numbers k such that phi(k - 2) = phi(k) - 2.

5, 7, 8, 13, 14, 16, 19, 20, 22, 31, 43, 46, 61, 64, 73, 94, 103, 109, 118, 139, 151, 166, 181, 193, 199, 214, 229, 241, 256, 271, 283, 313, 334, 349, 358, 421, 433, 454, 463, 523, 526, 571, 601, 619, 643, 661, 694, 718, 766, 811, 823, 829, 859, 883, 934, 958

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001838(n)+2. - Robert Israel, Oct 30 2018

Example

7 is in the sequence because phi(5) = 4 = phi(7) - 2.
8 is in the sequence because phi(6) = 2 = phi(8) - 2.
9 is not in the sequence because phi(7) = 6 but phi(9) - 2 = 4 instead.

Maple

with(numtheory): select(k->phi(k-2)=phi(k)-2, [$1..960]); # Muniru A Asiru, Oct 28 2018

Mathematica

Select[Range@1000, EulerPhi@(# - 2) == EulerPhi[#] - 2 &]
Flatten[Position[Partition[EulerPhi[Range[1000]], 3, 1], _?(#[[1]]==#[[3]]-2&), 1, Heads->False]]+2 (* Harvey P. Dale, Oct 24 2020 *)

Prog

(Magma) [n: n in [3..1000] | EulerPhi(n-2) eq EulerPhi(n)-2];
(PARI) isok(n) = eulerphi(n-2) == eulerphi(n)-2; \\ Michel Marcus, Oct 14 2018
(GAP) Filtered([1..960], k->Phi(k-2)=Phi(k)-2); # Muniru A Asiru, Oct 28 2018

Crossrefs

Cf. A001838. Contains A006512 and terms > 10 in A194593.

Sequence in context: A356897 A314374 A066001 * A047477 A216555 A288151

Adjacent sequences: A320388 A320389 A320390 * A320392 A320393 A320394

Keyword

nonn

Author

Vincenzo Librandi, Oct 13 2018

Status

approved