

A358719


A sequence of primes starting with p_1 = 2, p_2 = 3, p_3 = 5, p_4 = 11, p_5 = 13, p_6 = 23, such that, for i >= 7, (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 p_1*p_2*...*p_(i1).


2



2, 3, 5, 11, 13, 23, 19, 37, 73, 109, 131, 229, 457, 571, 1459, 1481, 2179, 2621, 2917, 2963, 4357, 8713, 49921, 1318901, 3391489, 6782977, 13565953
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OFFSET

1,1


COMMENTS

The sequence was used, together with A358717 and A358718, 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.
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*d1 as a candidate for a(28).  Max Alekseyev, Feb 19 2024


LINKS



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

The sequence is a slight modification of A358717.


KEYWORD

nonn,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



