A279241 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.

1601, 1447, 1301, 1163, 1033, 911, 797, 691, 593, 503, 421, 347, 281, 223, 173, 131, 97, 71, 53, 43, 41, 47, 61, 83, 113, 151, 197, 251, 313, 383, 461, 547, 641, 743, 853, 971, 1097, 1231, 1373, 1523

Offset: 1

Author

Charles Kusniec, Dec 08 2016

Keywords

• fini
• nonn

Comments

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

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

Crossrefs

Cf. A005846, A014556, A145096.

Programs

Maple

s1:=[]; f:=n->4*n^2+2*n+41;
for n from -20 to 19 do if isprime(abs(f(n))) then s1:=[op(s1), abs(f(n))]; fi; od:
s1; # From N. J. A. Sloane, Dec 17 2016. This does nothing more than produce the primes mentioned in the definition

Extensions

Edited by N. J. A. Sloane, Dec 17 2016