A179187 - OEIS

%I #31 Sep 08 2022 08:45:54

%S 5,9,15,21,15556,21016,25930,25935,27027,36304,46683,129675,266128,

%T 307923,329175,430348,503139,636400,684411,812170,1014778,1252713,

%U 1777545,1871788,1892452,1911987,2622160,2629930,2731360,2947035,3397480,4200100,5451537

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

%C There are only 43 terms below 10^7, and 1843 terms below 10^12. [_Jud McCranie_, Feb 13 2012]

%H Jud McCranie, <a href="/A179187/b179187.txt">Table of n, a(n) for n = 1..1843</a> (terms < 10^12)

%H F. Firoozbakht, <a href="http://www.primepuzzles.net/puzzles/puzz_466.htm">Puzzle 466. phi(n-1)=phi(n)=phi(n+1)</a>, in C. Rivera's Primepuzzles.

%H Kevin Ford, <a href="https://arxiv.org/abs/2002.12155">Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k)</a>, arXiv:2002.12155 [math.NT], 2020.

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

%t Select[Range[5000000], EulerPhi[#] == EulerPhi[# + 5] &] (* _Vincenzo Librandi_, Sep 08 2016 *)

%t Position[Partition[EulerPhi[Range[55*10^5]],6,1],_?(#[[1]] == #[[6]]&), {1}, Heads->False]//Flatten (* _Harvey P. Dale_, Nov 10 2016 *)

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

%o (Magma) [n: n in [1..5000000] | EulerPhi(n) eq EulerPhi(n+5)]; // _Vincenzo Librandi_, Sep 08 2016

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

%K nonn

%O 1,1

%A _M. F. Hasler_, Jan 05 2011