

A358717


A sequence of sorted primes 2 = p_1 < p_2 < ... < p_m such that (p_i + 1)/2 divides the product p_1*p_2*...*p_(i1) of the earlier primes and each prime factor of (p_i1)/2 is a prime factor of the product.


2



2, 3, 5, 11, 19, 37, 73, 109, 1459, 2179, 2917, 4357, 8713
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OFFSET

1,1


COMMENTS

The sequence was used, together with A358718 and A358719, by Ferrari and Sillari (Preprint2022) to prove that there are at least three solutions n to phi(n+k) = 2* phi(n) for all even k <= 4*10^58.
I have checked up to 10^8 and found no more terms.
Prime a(14) does not exist, which can be established by going over the divisors d of the product a(1)*...*a(13) and testing 2*d1 as a candidate for a(14).  Max Alekseyev, Feb 19 2024


LINKS



MATHEMATICA

s = {2}; step[s_] := Module[{p = NextPrime[s[[1]]], r = Times @@ s}, While[! Divisible[r, (p + 1)/2]  ! Divisible[r, Times @@ FactorInteger[(p  1)/2][[;; , 1]]], p = NextPrime[p]]; Join[s, {p}]]; Nest[step, s, 12] (* Amiram Eldar, Nov 30 2022 *)


CROSSREFS



KEYWORD

nonn,full,fini


AUTHOR



EXTENSIONS



STATUS

approved



