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

%I A282319 #40 Jul 28 2017 18:23:11
%S A282319 41,43,47,53,53,71,53,53,71,53,131,173,61,53,113,53,281,71,47,53,347,
%T A282319 131,347,173,53,347,71,53,151,593,547,421,461,281,53,593,83,503,347,
%U A282319 53,197,347,97,1033,593,347,313,1301,53,53,1097,1933,2203,71
%N A282319 a(n) = (2097203 mod n)^2 + (2097203 mod n) + 41.
%C A282319 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.
%H A282319 Frederic Isenmann, <a href="/A282319/a282319.txt">Table of n, a(n) for n=1..168.</a>
%e A282319 For n = 23, a(23) = 17^2+17+41 = 347, and 347 is prime.
%t A282319 Table[#^2 + # + 41 &@ Mod[2097203 , n], {n, 54}] (* _Michael De Vlieger_, Feb 12 2017 *)
%t A282319 f[n_]:=Module[{x=Mod[2097203,n]},x^2+x+41]; Array[f,60] (* _Harvey P. Dale_, Jul 28 2017 *)
%o A282319 (Python)
%o A282319 def formul(i):
%o A282319     return ((i*i+2097203)%i)*((i*i+2097203)%i)+((i*i+2097203)%i)+41
%o A282319 for i in range(1, 169):
%o A282319     n=formul(i)
%o A282319     print(n, end=", ")
%o A282319 (PARI) a(n)=subst(x^2+x+41,x,2097203%n) \\ _Charles R Greathouse IV_, Feb 14 2017
%Y A282319 Cf. A005846, A202018.
%K A282319 easy,nonn
%O A282319 1,1
%A A282319 _Frederic Isenmann_, Feb 11 2017