A056772 Numbers n such that phi(n+4) = phi(n) + 4.

3, 7, 12, 13, 18, 19, 24, 28, 36, 37, 40, 43, 66, 67, 79, 88, 97, 103, 109, 124, 127, 163, 184, 193, 223, 229, 232, 277, 307, 313, 328, 349, 379, 397, 424, 439, 457, 463, 487, 499, 508, 613, 643, 664, 673, 712, 739, 757, 769, 823, 853, 859, 877, 883, 904, 907

Offset

1,1

Comments

In contrast with A015913, composite solutions are not rare. Prime solutions are common.

From Kevin J. Gomez, Mar 02 2016: (Start)

Composite solutions have two known forms:

n such that n = 4 * (2^p - 1) where 2^p - 1 is a Mersenne prime. (A001348)

n such that n = 8q where q is a Sophie Germain prime. (A005394)

There are composite solutions (such as 36) that do not fit either of these forms.

(End)

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Example

n=1048: phi(1048)=520, phi(1048+4)=524.

Mathematica

Select[Range@1000, EulerPhi@(# + 4)== EulerPhi[#] + 4 &] (* Vincenzo Librandi, Sep 11 2015 *)
Position[Partition[EulerPhi[Range[1000]], 5, 1], _?(#[[1]]+4==#[[5]]&), 1, Heads-> False]//Flatten (* Harvey P. Dale, Dec 18 2019 *)

Prog

(PARI) isok(n) = eulerphi(n+4) == eulerphi(n) + 4; \\ Michel Marcus, Sep 11 2015
(Magma) [n: n in [1..1000] | EulerPhi(n+4) eq EulerPhi(n)+4]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Cf. A015913 (sigma(n+4) = sigma(n) + 4).

Cf. A001838 (k=2), this sequence (k=4), A262084 (k=6), A262085 (k=8), A262086 (k=10).

Sequence in context: A243705 A057927 A298788 * A024614 A230109 A045134

Adjacent sequences: A056769 A056770 A056771 * A056773 A056774 A056775

Keyword

nonn

Author

Labos Elemer, Aug 17 2000

Status

approved