login
Numbers n such that phi(n + 10) = phi(n) + 10 where phi(n) = A000010(n) is Euler's totient function.
4

%I #35 Sep 08 2022 08:46:13

%S 3,7,13,19,31,36,37,43,61,73,79,97,103,127,139,157,163,181,223,229,

%T 241,271,283,307,337,349,373,379,409,421,433,439,457,499,547,577,607,

%U 631,643,673,691,709,733,751,787,811,829,853,877,919,937,967

%N Numbers n such that phi(n + 10) = phi(n) + 10 where phi(n) = A000010(n) is Euler's totient function.

%C The only composite term less than 10^11 is 36. - _Giovanni Resta_, Sep 14 2015

%H Seiichi Manyama, <a href="/A262086/b262086.txt">Table of n, a(n) for n = 1..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>

%e 3 is in the sequence since phi(13) = phi(3) + 10.

%t Select[Range@1000, EulerPhi@(# + 10) == EulerPhi[#] + 10 &] (* _Vincenzo Librandi_, Sep 11 2015 *)

%o (Magma) [n: n in [1..1000] | EulerPhi(n+10) eq EulerPhi(n)+10]; // _Vincenzo Librandi_, Sep 11 2015

%o (PARI) is(n)=eulerphi(n + 10) == eulerphi(n) + 10 \\ _Anders Hellström_, Sep 11 2015

%Y Cf. A000010, A023203.

%Y Cf. A001838 (k=2), A056772 (k=4), A262084 (k=6), A262085 (k=8), this sequence (k=10).

%K nonn,easy

%O 1,1

%A _Kevin J. Gomez_, Sep 10 2015