The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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_(i-1) of the earlier primes and each prime factor of (p_i-1)/2 is a prime factor of the product p_1*p_2*...*p_(i-1). 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=1..27. 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 Similar to A001259. The sequence is a slight modification of A358717. Cf. A358718. Sequence in context: A228445 A287164 A020607 * A235631 A180640 A128425 Adjacent sequences: A358716 A358717 A358718 * A358720 A358721 A358722 KEYWORD nonn,fini,full AUTHOR Lorenzo Sillari, Nov 28 2022 EXTENSIONS Keywords 'full' and 'fini' added by Max Alekseyev, Feb 19 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 5 17:52 EDT 2024. Contains 374954 sequences. (Running on oeis4.)