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A105126 Primes of the form 16n+9. 22
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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 *)

PROG

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

CROSSREFS

Cf. A002145, A007521, A105127-A105132.

Sequence in context: A289982 A054806 A057540 * A214643 A142038 A213047

Adjacent sequences:  A105123 A105124 A105125 * A105127 A105128 A105129

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified June 2 07:55 EDT 2020. Contains 334767 sequences. (Running on oeis4.)