A352912 Irregular triangle read by rows: row n (n>=1) lists the primes of the form prime(n) + k! for k >= 0.

3, 3, 5, 7, 11, 29, 13, 31, 127, 727, 13, 17, 131, 5051, 3628811, 19, 37, 733, 19, 23, 41, 137, 362897, 39916817, 43, 139, 739, 5059, 3628819, 39916819, 87178291219, 29, 47, 743, 40343, 362903, 20922789888023, 31, 53, 149, 39916829, 479001629, 2432902008176640029, 37, 151, 751, 40351, 362911, 39916831, 355687428096031, 51090942171709440031, 1124000727777607680031

Offset: 1

Author

Editors of OEIS, based on a suggestion from Hemjyoti Nath, Apr 16 2022

Keywords

• nonn
• tabf

Examples

			The initial rows, prefixed by prime(n), are:
[2]: 3, 3,
[3]: 5,
[5]: 7, 11, 29,
[7]: 13, 31, 127, 727,
[11]: 13, 17, 131, 5051, 3628811,
[13]: 19, 37, 733,
[17]: 19, 23, 41, 137, 362897, 39916817,
[19]: 43, 139, 739, 5059, 3628819, 39916819, 87178291219,
[23]: 29, 47, 743, 40343, 362903, 20922789888023,
[29]: 31, 53, 149, 39916829, 479001629, 2432902008176640029,
[31]: 37, 151, 751, 40351, 362911, 39916831, 355687428096031, 51090942171709440031, 1124000727777607680031,
[37]: 43, 61, 157, 757, 5077, 40357, 39916837, 6402373705728037, 2432902008176640037, 51090942171709440037, 8683317618811886495518194401280000037,
...
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1019

Crossrefs

Cf. A352913 (last term in each row), A082470 (lengths of rows).

Programs

PARI

forprime(p=2,59,print1([p],": ");for(k=0,p,if(ispseudoprime(p+k!),print1(p+k!,", ")));print())

Python

from sympy import isprime, prime
from itertools import count, islice
def agen(): # generator of terms
    for n in count(1):
        pn, fk = prime(n), 1
        for k in range(1, pn+1):
            if isprime(pn + fk): yield pn + fk
            fk *= k
print(list(islice(agen(), 51))) # Michael S. Branicky, Apr 16 2022