A282319 a(n) = (2097203 mod n)^2 + (2097203 mod n) + 41.

41, 43, 47, 53, 53, 71, 53, 53, 71, 53, 131, 173, 61, 53, 113, 53, 281, 71, 47, 53, 347, 131, 347, 173, 53, 347, 71, 53, 151, 593, 547, 421, 461, 281, 53, 593, 83, 503, 347, 53, 197, 347, 97, 1033, 593, 347, 313, 1301, 53, 53, 1097, 1933, 2203, 71

Offset: 1

Author

Frederic Isenmann, Feb 11 2017

Keywords

• easy
• nonn

Comments

This sequence gives 168 prime numbers for n=1 to 168 with 63 different primes. This formula is based on the lucky numbers of Euler.

Examples

			For n = 23, a(23) = 17^2+17+41 = 347, and 347 is prime.
		

Links

• Frederic Isenmann, Table of n, a(n) for n=1..168.

Crossrefs

Cf. A005846, A202018.

Programs

Mathematica

Table[#^2 + # + 41 &@ Mod[2097203 , n], {n, 54}] (* Michael De Vlieger, Feb 12 2017 *)
f[n_]:=Module[{x=Mod[2097203,n]},x^2+x+41]; Array[f,60] (* Harvey P. Dale, Jul 28 2017 *)

PARI

a(n)=subst(x^2+x+41,x,2097203%n) \\ Charles R Greathouse IV, Feb 14 2017

Python

def formul(i):
    return ((i*i+2097203)%i)*((i*i+2097203)%i)+((i*i+2097203)%i)+41
for i in range(1, 169):
    n=formul(i)
    print(n, end=", ")