A271660 - OEIS

A271660

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

5, 17, 257, 317, 977, 2237, 3257, 5189, 8537, 9533, 11717, 13367, 22937, 37847, 65537, 76871, 307397, 428957, 491537, 589409, 610913, 983777, 1055063, 1207097, 1340789, 1659587, 2822717, 3137357, 3264887, 3488333, 4994117, 5577827, 6475457, 7378373, 7479089

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The first 4 known Fermat primes > 3 from A019434 are in the sequence.

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

317 is a term because phi(phi(317-2)-1) = phi(phi(315)-1) = phi(144-1) = phi(143) = 120 = phi(phi(317-1)-1) = phi(phi(316)-1) = phi(156-1) = phi(155).

MATHEMATICA

Select[Prime@ Range[3, 10^6], EulerPhi[EulerPhi[# - 2] - 1] == EulerPhi[EulerPhi[# - 1] - 1] &] (* Michael De Vlieger, Apr 12 2016 *)

PROG

(Magma) [n: n in [4..5*10^7] | IsPrime(n) and EulerPhi(EulerPhi(n-2)-1) eq EulerPhi(EulerPhi(n-1)-1)]

(PARI) lista(nn) = forprime(p=5, nn, if(eulerphi(eulerphi(p-2)-1) == eulerphi(eulerphi(p-1)-1), print1(p, ", "))); \\ Altug Alkan, Apr 12 2016

CROSSREFS

Cf. A019434, A271655, A271656, A271657, A271658, A271659.

Sequence in context: A089894 A077718 A235461 * A273948 A271657 A273999

Adjacent sequences: A271657 A271658 A271659 * A271661 A271662 A271663

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Apr 12 2016

STATUS

approved