cp's OEIS Frontend

A179189 Numbers n such that phi(n) = phi(n+7), with Euler's totient function phi = A000010.

%I A179189 #35 Sep 08 2022 08:45:54
%S A179189 5,7,21,45,75,105,285,488,585,765,1148,1275,1358,1785,2528,3465,4088,
%T A179189 6825,9405,12375,14348,15345,16208,16988,23648,25905,25935,42698,
%U A179189 50018,52845,54615,61448,62865,68445,78195,80025,82005,88328,93555,98475
%N A179189 Numbers n such that phi(n) = phi(n+7), with Euler's totient function phi = A000010.
%C A179189 There are 40 terms below 10^5, 81 terms below 10^6 and 162 terms below 10^7.  There are 6606 terms below 10^12. [_Jud McCranie_, Feb 13 2012]
%C A179189 _Farideh Firoozbakht_ asks whether there is some a(n+1) = a(n)+7, cf. link.
%C A179189 For n < 10^13, the only n such that phi(n-7) = phi(n) = phi(n+7) is 30057431145. - _Giovanni Resta_, Feb 27 2014
%H A179189 Jud McCranie, <a href="/A179189/b179189.txt">Table of n, a(n) for n = 1..6606</a> (terms < 10^12)
%H A179189 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 A179189 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 A179189 A000010(a(n)) = A000010(a(n)+7).
%t A179189 Select[Range[100000], EulerPhi[#] == EulerPhi[# + 7] &] (* _Vincenzo Librandi_, Sep 08 2016 *)
%o A179189 (PARI) {op=vector(N=7); for( n=1, 1e5, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}
%o A179189 (Magma) [n: n in [1..100000] | EulerPhi(n) eq EulerPhi(n+7)]; // _Vincenzo Librandi_, Sep 08 2016
%Y A179189 Cf. A000010, A001274, A001494, A179186, A179187, A179188, A007015.
%K A179189 nonn
%O A179189 1,1
%A A179189 _M. F. Hasler_, Jan 05 2011