Smaller twin prime p such that phi(p-1) = phi(p+1), where phi is Euler’s totient function.
5, 11, 71, 2591, 208391, 16692551, 48502931, 92012201, 249206231, 419445251, 496978301, 1329067391, 1837151681, 2277479051, 2647600061, 4733566391, 6435087011, 10327948751, 2277479051, 2647600061
1
Note that equality occurs very rarely. Garcia et al. prove in their theorem 3 that the number of primes p <= x in this sequence is O(x/exp((log x)^(1/3))).
T. D. Noe, Plot of 20 terms
Stephan Ramon Garcia, Elvis Kahoro, and Florian Luca, Primitive root discrepancy for twin primes, arXiv 1705.02485 (May 06 2017)
(Mma) t = {}; n = 0; While[Length[t] < 5, n++; p = Prime[n]; If[PrimeQ[p + 2] && EulerPhi[p - 1] == EulerPhi[p + 1], AppendTo[t, p]]]; t
nonn,hard,more
T. D. Noe, May 09 2017