A356847 - OEIS

%I #31 Mar 05 2023 13:30:45

%S 5,7,13,67,97,9337,28657,516157,2193637,1725215287,5858906527,

%T 10845974467,311697041437,2748104242057,478834469031547,

%U 30509330585363257

%N Greedily choose a(n) to be the least prime p > a(n-1) such that all sums a(i) + a(j) - 1, 1 <= i < j, are also prime.

%C It is not known if this sequence is infinite.

%H Sequence inspired by (but not mentioned in) <a href="https://www.ntwebseminar.org/#h.7czbb89r8z9">talk</a> by Terence Tao, February 23 2023, in the Number Theory Web Seminar.

%o (Python)

%o from math import gcd

%o from itertools import count, islice

%o from sympy import isprime, nextprime

%o def agen(): # generator of terms

%o     alst = [5]

%o     while True:

%o         yield alst[-1]

%o         p = nextprime(alst[-1])

%o         while any(not isprime(ai + p - 1) for ai in alst):

%o             p = nextprime(p)

%o         alst.append(p)

%o print(list(islice(agen(), 9))) # _Michael S. Branicky_, Feb 23 2023

%K nonn,more

%O 1,1

%A _Jeffrey Shallit_, Feb 23 2023

%E a(10)-a(12) from _Michael S. Branicky_, Feb 23 2023

%E a(13) from _Rémy Sigrist_, Feb 24 2023

%E a(14)-a(16) from _Bert Dobbelaere_, Mar 05 2023