A380026 -id:A380026 - cp's OEIS frontend

Showing 1-1 of 1 results.

A380027 a(n) is the largest prime p such that p - a(n-1) is a primorial, starting with a(1) = 2.

Original entry on oeis.org

2, 3, 5, 11, 41, 9699731

Offset: 1

Hayden Chesnut, Jan 09 2025

nonn

From Michael S. Branicky, Jan 11 2025: (Start)
The corresponding k are such that 0 <= k < PrimePi(P), so a(n-1)+1 <= a(n) <= a(n-1)+primorial(PrimePi(a(n-1))-1).
a(7) >= 9699731 + primorial(452), which is prime and has 1351 digits, so it is too large to include, even in a b-file. (End)

			a(3) = 5
For primes less than 5+5#:
31 - 5 = 26 is not in A002110
...
13 - 5 = 8 is not in A002110
11 - 5 = 6 is in A002110 so a(4) = 11

Cf. A002110, A265109, A380026.

from itertools import count, islice
from sympy import isprime, primepi, 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 range(primepi(an)-1, -1, -1) if isprime(s:=an+A002110(k)))
print(list(islice(agen(), 6))) # Michael S. Branicky, Jan 11 2025

a(n) = a(n-1) + A002110(A265109(A000720(a(n-1)))), for n > 1. - Michael S. Branicky, Jan 10 2025

Showing 1-1 of 1 results.