A094407 Primes of the form 16n+1.

17, 97, 113, 193, 241, 257, 337, 353, 401, 433, 449, 577, 593, 641, 673, 769, 881, 929, 977, 1009, 1153, 1201, 1217, 1249, 1297, 1361, 1409, 1489, 1553, 1601, 1697, 1777, 1873, 1889, 2017, 2081, 2113, 2129, 2161, 2273, 2417, 2593, 2609, 2657, 2689, 2753

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jun 03 2004

Keywords

• nonn
• easy

Comments

Subsequence of A007519 (primes of form 8n+1). - Zak Seidov, May 16 2012

Primes p such that p XOR 14 = p + 14. - Brad Clardy, Jul 23 2012

A prime of the form 16n+1 is represented either by both x^2+32y^2 and x^2+64y^2 or by neither (see Kaplansky link). - Michel Marcus, Dec 23 2012

Odd primes p such that -1 is an 8th power mod p. - Eric M. Schmidt, Mar 27 2014

Links

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

Crossrefs

Primes congruent to k mod 16: A094407, A091968, A127589, A141194, A105126, A141195, A141196, A127576.

Cf. A065091, A002144, A007519, A133870, A142925, A208177, A208178, A076339.

Programs

Haskell

a094407 n = a094407_list !! (n-1)
a094407_list = filter ((== 1) . a010051) [1,17..]
-- Reinhard Zumkeller, Mar 06 2012

Maple

p:=proc(n) if isprime(16*n+1)=true then 16*n+1 else fi end:seq(p(n),n=1..200); # Emeric Deutsch, Dec 23 2004

Mathematica

lst={};Do[p=16*n+1;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 26 2009 *)
Select[16*Range[200]+1,PrimeQ] (* Harvey P. Dale, Nov 04 2017 *)

Extensions

More terms from Emeric Deutsch, Dec 23 2004