A266164 Primes p such that phi(p) = phi(p-2) + phi(p-1); Phibonacci primes.

3, 5, 7, 11, 17, 23, 37, 41, 47, 101, 137, 233, 257, 857, 1297, 1601, 2017, 4337, 14401, 16097, 30497, 62801, 65537, 77617, 686737, 18800897, 255080417, 12885295097, 12918324737, 96052225601, 516392008697, 7026644072737

Offset: 1

Author

Jaroslav Krizek, Dec 22 2015

Keywords

• nonn
• changed

Comments

Primes from A065557; complement of A065572 with respect to A065557.

The first 5 known Fermat primes from A019434 are in sequence.

Examples

			17 is in this sequence because phi(17) = phi(15) + phi(16); 16 = 8 + 8.
		

Crossrefs

Cf. A000010, A065557, A065572.

Programs

Magma

[n: n in [3..5*10^7] | IsPrime(n) and EulerPhi(n) eq EulerPhi(n-2)+ EulerPhi(n-1)]

Maple

select(t -> isprime(t) and t-1 = numtheory:-phi(t-1) + numtheory:-phi(t-2), [seq(i,i=3..10^6,2)]); # Robert Israel, Dec 22 2015

Mathematica

Select[Prime[Range[56000]],EulerPhi[#]==EulerPhi[#-2]+EulerPhi[#-1]&] (* The program generates the first 26 terms of the sequence. *) (* Harvey P. Dale, Aug 22 2025 *)