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A256510 Primes p such that phi(p-2) = phi(p-1).

%I A256510 #22 Jul 16 2025 20:47:43
%S A256510 3,5,17,257,977,3257,5189,11717,13367,22937,65537,307397,491537,
%T A256510 589409,983777,1659587,2822717,3137357,5577827,6475457,7378373,
%U A256510 8698097,10798727,32235737,37797437,39220127,39285437,51555137,52077197,56992553,63767927,70075997
%N A256510 Primes p such that phi(p-2) = phi(p-1).
%C A256510 First 5 Fermat primes from A019434 are terms of this sequence.
%C A256510 a(2) = 5 is only term of a(n) such that a(n) - 2 is a prime q, i.e., prime 3 is only prime q such that phi(q) = phi(q+1).
%C A256510 If there are any other Fermat primes, they will not be in the sequence. - _Robert Israel_, Mar 31 2015
%H A256510 Amiram Eldar, <a href="/A256510/b256510.txt">Table of n, a(n) for n = 1..819</a> (terms below 10^13, calculated from the b-file at A001274)
%e A256510 Prime 17 is in the sequence because phi(15) = phi(16) = 8.
%p A256510 with(numtheory): A256510:=n->`if`(isprime(n) and phi(n-2) = phi(n-1), n, NULL): seq(A256510(n), n=1..10^5); # _Wesley Ivan Hurt_, Mar 31 2015
%t A256510 Select[Prime@ Range@ 100000, EulerPhi[# - 2] == EulerPhi[# - 1] &] (* _Michael De Vlieger_, Mar 31 2015 *)
%o A256510 (Magma) [n: n in [3..10^7] |  IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)];
%Y A256510 Cf. A000010, A000215, A001274, A019434.
%K A256510 nonn
%O A256510 1,1
%A A256510 _Jaroslav Krizek_, Mar 31 2015