A067933 -id:A067933 - cp's OEIS frontend

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

Amiram Eldar, Apr 26 2018

nonn

Intersection of A001359 and A067890 (or A066812).

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

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

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.

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

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

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

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

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

A119388 Numbers n such that n == -1 (mod phi(n-1)).

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 511, 2591, 131071, 3359231, 167247871, 8589934591

Offset: 1

Jorge Coveiro, Jul 25 2006

nonn

This sequence has the terms from A067933 (all primes), plus 511 and 3359231 that are not primes.
Checked up to x<70000000
a(14) > 10^11. [From Donovan Johnson, Aug 08 2010]

Cf. A067933.

for(x=1,70000000,if(((x)+1)%eulerphi((x)-1)==0,print((x))))

a(13) from Donovan Johnson, Aug 08 2010

cp's OEIS Frontend

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

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