cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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%I A303549 #14 Apr 28 2018 13:12:34
%S A303549 5,11,71,2591,208391,16692551,48502931,92012201,249206231,419445251,
%T A303549 496978301,1329067391,1837151681,2277479051,2647600061,4733566391,
%U A303549 6435087011,10327948751,14089345691,14923624031,22415286251,27508270301,39662281331,59013882071,70353395351
%N A303549 Lesser of twin primes p for which phi(p-1) = phi(p+1), where phi(n) is the Euler totient function (A000010).
%C A303549 Intersection of A001359 and A067890 (or A066812).
%C A303549 The terms below 10^8 were taken from the paper by Garcia et al.
%H A303549 Stephan Ramon Garcia, Elvis Kahoro and Florian Luca, <a href="https://doi.org/10.1080/10586458.2017.1360809">Primitive root bias for twin primes</a>, Experimental Mathematics (2017), pp. 1-10, <a href="http://pages.pomona.edu/~sg064747/PAPERS/PRBTP.pdf">alternative link</a>, preprint, <a href="https://arxiv.org/abs/1705.02485">arXiv:1705.02485</a> [math.NT], 2017.
%e A303549 p = 5 is the lesser of the twin primes (5, 7), and phi(5-1) = phi(5+1) = 2.
%t A303549 seq={}; Do[p = Prime[i]; If[PrimeQ[p+2] && EulerPhi[p-1] == EulerPhi[p+1], AppendTo[seq, p]], {i, 1, 1000000}]; seq
%o A303549 (PARI) isok(p) = isprime(p) && isprime(p+2) && (eulerphi(p-1) == eulerphi(p+1)); \\ _Michel Marcus_, Apr 26 2018
%Y A303549 Cf. A000010, A001359, A006512, A008330, A066812, A067890, A067933, A286714, A286715.
%K A303549 nonn
%O A303549 1,1
%A A303549 _Amiram Eldar_, Apr 26 2018
%E A303549 a(12)-a(16) from _Michel Marcus_, Apr 26 2018
%E A303549 a(17)-a(25) from _Giovanni Resta_, Apr 26 2018