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

1,1

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

Links

Table of n, a(n) for n=1..40.

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

Crossrefs

Cf. A005846, A014556, A145096.

Sequence in context: A206250 A187241 A323496 * A060566 A078853 A078958

Adjacent sequences: A279238 A279239 A279240 * A279242 A279243 A279244

Keyword

fini,nonn

Author

Charles Kusniec, Dec 08 2016

Extensions

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

Status

approved