A105126 Primes of the form 16n+9.

41, 73, 89, 137, 233, 281, 313, 409, 457, 521, 569, 601, 617, 761, 809, 857, 937, 953, 1033, 1049, 1097, 1129, 1193, 1289, 1321, 1433, 1481, 1609, 1657, 1721, 1753, 1801, 1913, 1993, 2089, 2137, 2153, 2281, 2297, 2377, 2393, 2441, 2473, 2521, 2617, 2633, 2713

Offset: 1

Author

N. J. A. Sloane, based on correspondence from Marco Matosic, Apr 11 2005

Keywords

• nonn

Comments

A prime of the form 16n+9 is represented by exactly one of x^2 + 32y^2 and x^2 + 64y^2 (see Kaplanski link). - Michel Marcus, Dec 23 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Irving Kaplansky, The forms x+32y^2 and x+64y^2, Proc. Amer. Math. Soc. 131 (2003), 2299-2300

Crossrefs

Cf. A002145, A007521, A105127-A105132.

Programs

Maple

M:=500; f:=proc(n) local t1,t2; t1:=[]; for k from 0 to M do t2:=2^n*k+2^(n-1)+1; if isprime(t2) then t1:=[op(t1),t2]; fi; od; t1; end; f(4);

Mathematica

lst={};Do[p=16*n+9;If[PrimeQ[p],AppendTo[lst,p]],{n,0,3*5!,1}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)

PARI

select(n->n%16==9, primes(500)) \\ Charles R Greathouse IV, Apr 29 2015