A303549 Lesser of twin primes p for which phi(p-1) = phi(p+1), where phi(n) is the Euler totient function (A000010).

5, 11, 71, 2591, 208391, 16692551, 48502931, 92012201, 249206231, 419445251, 496978301, 1329067391, 1837151681, 2277479051, 2647600061, 4733566391, 6435087011, 10327948751, 14089345691, 14923624031, 22415286251, 27508270301, 39662281331, 59013882071, 70353395351

Offset

1,1

Comments

Intersection of A001359 and A067890 (or A066812).

The terms below 10^8 were taken from the paper by Garcia et al.

Links

Table of n, a(n) for n=1..25.

Stephan Ramon Garcia, Elvis Kahoro and Florian Luca, Primitive root bias for twin primes, Experimental Mathematics (2017), pp. 1-10, alternative link, preprint, arXiv:1705.02485 [math.NT], 2017.

Example

p = 5 is the lesser of the twin primes (5, 7), and phi(5-1) = phi(5+1) = 2.

Mathematica

seq={}; Do[p = Prime[i]; If[PrimeQ[p+2] && EulerPhi[p-1] == EulerPhi[p+1], AppendTo[seq, p]], {i, 1, 1000000}]; seq

Prog

(PARI) isok(p) = isprime(p) && isprime(p+2) && (eulerphi(p-1) == eulerphi(p+1)); \\ Michel Marcus, Apr 26 2018

Crossrefs

Cf. A000010, A001359, A006512, A008330, A066812, A067890, A067933, A286714, A286715.

Sequence in context: A328453 A175207 A067890 * A192436 A154797 A161852

Adjacent sequences: A303546 A303547 A303548 * A303550 A303551 A303552

Keyword

nonn

Author

Amiram Eldar, Apr 26 2018

Extensions

a(12)-a(16) from Michel Marcus, Apr 26 2018

a(17)-a(25) from Giovanni Resta, Apr 26 2018

Status

approved