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

3, 5, 17, 257, 977, 3257, 5189, 11717, 13367, 22937, 65537, 307397, 491537, 589409, 983777, 1659587, 2822717, 3137357, 5577827, 6475457, 7378373, 8698097, 10798727, 32235737, 37797437, 39220127, 39285437, 51555137, 52077197, 56992553, 63767927, 70075997

Offset: 1

Author

Jaroslav Krizek, Mar 31 2015

Keywords

• nonn

Comments

First 5 Fermat primes from A019434 are terms of this sequence.

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).

If there are any other Fermat primes, they will not be in the sequence. - Robert Israel, Mar 31 2015

Examples

			Prime 17 is in the sequence because phi(15) = phi(16) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..819 (terms below 10^13, calculated from the b-file at A001274)

Crossrefs

Cf. A000010, A000215, A001274, A019434.

Programs

Magma

[n: n in [3..10^7] |  IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)];

Maple

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

Mathematica

Select[Prime@ Range@ 100000, EulerPhi[# - 2] == EulerPhi[# - 1] &] (* Michael De Vlieger, Mar 31 2015 *)