A179187 Numbers n such that phi(n)=phi(n+5), with Euler's totient function phi=A000010.

5, 9, 15, 21, 15556, 21016, 25930, 25935, 27027, 36304, 46683, 129675, 266128, 307923, 329175, 430348, 503139, 636400, 684411, 812170, 1014778, 1252713, 1777545, 1871788, 1892452, 1911987, 2622160, 2629930, 2731360, 2947035, 3397480, 4200100, 5451537

Offset: 1

Author

M. F. Hasler, Jan 05 2011

Keywords

• nonn

Comments

There are only 43 terms below 10^7, and 1843 terms below 10^12. [Jud McCranie, Feb 13 2012]

Links

• Jud McCranie, Table of n, a(n) for n = 1..1843 (terms < 10^12)
• F. Firoozbakht, Puzzle 466. phi(n-1)=phi(n)=phi(n+1), in C. Rivera's Primepuzzles.
• Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.

Crossrefs

Cf. A000010, A001274, A001494, A179186, A007015.

Programs

Magma

[n: n in [1..5000000] | EulerPhi(n) eq EulerPhi(n+5)]; // Vincenzo Librandi, Sep 08 2016

Mathematica

Select[Range[5000000], EulerPhi[#] == EulerPhi[# + 5] &] (* Vincenzo Librandi, Sep 08 2016 *)
Position[Partition[EulerPhi[Range[55*10^5]],6,1],?(#[[1]] == #[[6]]&), {1}, Heads->False]//Flatten (* _Harvey P. Dale, Nov 10 2016 *)

PARI

{op=vector(N=5); for( n=1,1e7,if( op[n%N+1]+0==op[n%N+1]=eulerphi(n),print1(n-N,",")))}

Formula

A000010(a(n)) = A000010(a(n)+5).