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