A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.
1, 1, 1, 2, 1, 1, 2, 1, 3, 10, 3, 1, 2, 1, 1, 4, 1, 29, 14, 1, 1, 14, 2, 1, 2, 4, 1, 2, 4, 5, 12, 2, 1, 2, 2, 9, 16, 1, 2, 80, 1, 2, 4, 2, 3, 16, 2, 2, 2, 1, 15, 960, 15, 1, 4, 3, 1, 14, 1, 6, 20, 1, 3, 946, 6, 1, 18, 10, 1, 4, 1, 5, 42, 4, 1, 828, 1, 1, 2, 1, 12, 2, 6, 4, 30, 3, 3022, 2, 1, 1
Offset: 2
Keywords
Links
- Eric Chen, Table of n, a(n) for n = 2..122
- Gary Barnes, Sierpinski conjectures and proofs
- Eric Chen, Table n, a(n) for n = 2..360 status
Crossrefs
For the numbers k such that these forms are prime:
a1(b): numbers k such that (b-1)*b^k-1 is prime
a2(b): numbers k such that (b-1)*b^k+1 is prime
a3(b): numbers k such that (b+1)*b^k-1 is prime
a4(b): numbers k such that (b+1)*b^k+1 is prime (no such k exists when b == 1 (mod 3))
a5(b): numbers k such that b^k-(b-1) is prime
a6(b): numbers k such that b^k+(b-1) is prime
a7(b): numbers k such that b^k-(b+1) is prime
a8(b): numbers k such that b^k+(b+1) is prime (no such k exists when b == 1 (mod 3)).
Using "-------" if there is currently no OEIS sequence and "xxxxxxx" if no such k exists (this occurs only for a4(b) and a8(b) for b == 1 (mod 3)):
.
b a1(b) a2(b) a3(b) a4(b) a5(b) a6(b) a7(b) a8(b)
--------------------------------------------------------------------
13 A297348 ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
14 A273523 ------- ------- ------- ------- ------- ------- -------
15 ------- ------- ------- ------- ------- ------- ------- -------
16 ------- ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
Programs
-
PARI
a(n)=for(k=1,2^16,if(ispseudoprime((n-1)*n^k+1),return(k)))
Comments