A356847 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.

5, 7, 13, 67, 97, 9337, 28657, 516157, 2193637, 1725215287, 5858906527, 10845974467, 311697041437, 2748104242057, 478834469031547, 30509330585363257

Offset

1,1

Comments

It is not known if this sequence is infinite.

Links

Table of n, a(n) for n=1..16.

Sequence inspired by (but not mentioned in) talk by Terence Tao, February 23 2023, in the Number Theory Web Seminar.

Prog

(Python)
from math import gcd
from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    alst = [5]
    while True:
        yield alst[-1]
        p = nextprime(alst[-1])
        while any(not isprime(ai + p - 1) for ai in alst):
            p = nextprime(p)
        alst.append(p)
print(list(islice(agen(), 9))) # Michael S. Branicky, Feb 23 2023

Crossrefs

Sequence in context: A077781 A102872 A102873 * A342506 A158892 A106022

Adjacent sequences: A356844 A356845 A356846 * A356848 A356849 A356850

Keyword

nonn,more

Author

Jeffrey Shallit, Feb 23 2023

Extensions

a(10)-a(12) from Michael S. Branicky, Feb 23 2023

a(13) from Rémy Sigrist, Feb 24 2023

a(14)-a(16) from Bert Dobbelaere, Mar 05 2023

Status

approved