A380026 a(n) is the smallest prime p such that p - a(n-1) is a primorial, starting with a(1)=2.

2, 3, 5, 7, 13, 19, 229, 439, 2749, 5059, 7369, 9679, 39709, 42019, 6469735249, 5766152219975951659023630035336134306565384015606066326325804059, 5766152219975951659023630035336134306565384015606073747063938869, 5766152219975951659023630035336134306565384015606073747287031739

Offset: 1

Author

Hayden Chesnut, Jan 09 2025

Keywords

• nonn

Examples

			a(4) = 7
For primes greater than 7:
11 - 7 = 4 is not in A002110
13 - 7 = 6 is in A002110 so a(5) = 13
		

Crossrefs

Cf. A000720, A002110, A100380, A380027.

Programs

Python

from itertools import count, islice
from sympy import isprime, primorial
def A002110(n): return primorial(n) if n > 0 else 1
def agen(an=2): # generator of terms
    while True:
        yield an
        an = next(s for k in count(0) if isprime(s:=an+A002110(k)))
print(list(islice(agen(), 18))) # Michael S. Branicky, Jan 10 2025

Python

from sympy import isprime
import primesieve
it = primesieve.Iterator()
chain = [2]
pchain = []
n = 1
while len(chain) < 18:
    while True:
        p = it.next_prime()
        if isprime(chain[-1]+n):
            chain.append(chain[-1]+n)
            print(len(chain))
            break
        n *= p
    p = it.skipto(0)
    n = 1
print(chain) # Hayden Chesnut, Jan 10 2025

Formula

a(n) = a(n-1) + A002110(A100380(A000720(a(n-1)))), for n > 1. - Michael S. Branicky, Jan 10 2025