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Let f(n) = 4*n^2 + 2*n + 41. The values |f(n)| are primes for all n in the range -20 to 19 (but not for n=-21 or 20). The sequence lists this maximal run of primes in the order in which they appear.
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%I #15 Nov 22 2021 10:17:13

%S 1601,1447,1301,1163,1033,911,797,691,593,503,421,347,281,223,173,131,

%T 97,71,53,43,41,47,61,83,113,151,197,251,313,383,461,547,641,743,853,

%U 971,1097,1231,1373,1523

%N Let f(n) = 4*n^2 + 2*n + 41. The values |f(n)| are primes for all n in the range -20 to 19 (but not for n=-21 or 20). The sequence lists this maximal run of primes in the order in which they appear.

%C This same list will also appear for 0<=x<=39 using the form 4x^2-158x+1601.

%C The substitution 2n = m changes this quadratic form into Euler's famous quadratic form m^2+m+41 (see A005846). Concerning the conjectured extremal properties of these forms, one should note the comment from _T. D. Noe_ in A005846. For another quadratic form similar to this one, see A145096. - _N. J. A. Sloane_, Dec 17 2016

%p s1:=[]; f:=n->4*n^2+2*n+41;

%p for n from -20 to 19 do if isprime(abs(f(n))) then s1:=[op(s1), abs(f(n))]; fi; od:

%p s1; # From _N. J. A. Sloane_, Dec 17 2016. This does nothing more than produce the primes mentioned in the definition

%Y Cf. A005846, A014556, A145096.

%K fini,nonn

%O 1,1

%A _Charles Kusniec_, Dec 08 2016

%E Edited by _N. J. A. Sloane_, Dec 17 2016