OFFSET
1,1
COMMENTS
The sequence was used, together with A358717 and A358718, by Ferrari and Sillari (Preprint-2022) to prove that there are at least three solutions n to phi(n+k) = 2*phi(n) for all even k <= 4*10^58.
Prime a(28) does not exist, which can be established by going over the divisors d of the product a(1)*...*a(27) and testing 2*d-1 as a candidate for a(28). - Max Alekseyev, Feb 19 2024
LINKS
M. Ferrari and L. Sillari, On the minimal number of solutions of the equation phi(n+k) = M*phi(n), M=1,2, arXiv:2110.05401 [math.NT], 2021.
MATHEMATICA
s = {2, 3, 5, 11, 13, 23}; step[s_] := Module[{p = 7, r = Times @@ s}, While[MemberQ[s, p] || ! Divisible[r, (p + 1)/2] || ! Divisible[r, Times @@ FactorInteger[(p - 1)/2][[;; , 1]]], p = NextPrime[p]]; Join[s, {p}]]; Nest[step, s, 21] (* Amiram Eldar, Dec 01 2022 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Lorenzo Sillari, Nov 28 2022
EXTENSIONS
Keywords 'full' and 'fini' added by Max Alekseyev, Feb 19 2024
STATUS
approved