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

%I A352912 #17 Apr 26 2022 08:10:48
%S A352912 3,3,5,7,11,29,13,31,127,727,13,17,131,5051,3628811,19,37,733,19,23,
%T A352912 41,137,362897,39916817,43,139,739,5059,3628819,39916819,87178291219,
%U A352912 29,47,743,40343,362903,20922789888023,31,53,149,39916829,479001629,2432902008176640029,37,151,751,40351,362911,39916831,355687428096031,51090942171709440031,1124000727777607680031
%N A352912 Irregular triangle read by rows: row n (n>=1) lists the primes of the form prime(n) + k! for k >= 0.
%H A352912 Michael S. Branicky, <a href="/A352912/b352912.txt">Table of n, a(n) for n = 1..1019</a>
%e A352912 The initial rows, prefixed by prime(n), are:
%e A352912 [2]: 3, 3,
%e A352912 [3]: 5,
%e A352912 [5]: 7, 11, 29,
%e A352912 [7]: 13, 31, 127, 727,
%e A352912 [11]: 13, 17, 131, 5051, 3628811,
%e A352912 [13]: 19, 37, 733,
%e A352912 [17]: 19, 23, 41, 137, 362897, 39916817,
%e A352912 [19]: 43, 139, 739, 5059, 3628819, 39916819, 87178291219,
%e A352912 [23]: 29, 47, 743, 40343, 362903, 20922789888023,
%e A352912 [29]: 31, 53, 149, 39916829, 479001629, 2432902008176640029,
%e A352912 [31]: 37, 151, 751, 40351, 362911, 39916831, 355687428096031, 51090942171709440031, 1124000727777607680031,
%e A352912 [37]: 43, 61, 157, 757, 5077, 40357, 39916837, 6402373705728037, 2432902008176640037, 51090942171709440037, 8683317618811886495518194401280000037,
%e A352912 ...
%o A352912 (PARI)
%o A352912 forprime(p=2,59,print1([p],": ");for(k=0,p,if(ispseudoprime(p+k!),print1(p+k!,", ")));print())
%o A352912 (Python)
%o A352912 from sympy import isprime, prime
%o A352912 from itertools import count, islice
%o A352912 def agen(): # generator of terms
%o A352912     for n in count(1):
%o A352912         pn, fk = prime(n), 1
%o A352912         for k in range(1, pn+1):
%o A352912             if isprime(pn + fk): yield pn + fk
%o A352912             fk *= k
%o A352912 print(list(islice(agen(), 51))) # _Michael S. Branicky_, Apr 16 2022
%Y A352912 Cf. A352913 (last term in each row), A082470 (lengths of rows).
%K A352912 nonn,tabf
%O A352912 1,1
%A A352912 Editors of OEIS, based on a suggestion from _Hemjyoti Nath_, Apr 16 2022