Hayden Chesnut has authored 2 sequences.
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
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
-
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
A380026
a(n) is the smallest prime p such that p - a(n-1) is a primorial, starting with a(1)=2.
Original entry on oeis.org
2, 3, 5, 7, 13, 19, 229, 439, 2749, 5059, 7369, 9679, 39709, 42019, 6469735249, 5766152219975951659023630035336134306565384015606066326325804059, 5766152219975951659023630035336134306565384015606073747063938869, 5766152219975951659023630035336134306565384015606073747287031739
Offset: 1
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
-
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
-
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
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