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Primes of the form 16n+1.
22

%I #42 Apr 03 2023 10:36:10

%S 17,97,113,193,241,257,337,353,401,433,449,577,593,641,673,769,881,

%T 929,977,1009,1153,1201,1217,1249,1297,1361,1409,1489,1553,1601,1697,

%U 1777,1873,1889,2017,2081,2113,2129,2161,2273,2417,2593,2609,2657,2689,2753

%N Primes of the form 16n+1.

%C Subsequence of A007519 (primes of form 8n+1). - _Zak Seidov_, May 16 2012

%C Primes p such that p XOR 14 = p + 14. - _Brad Clardy_, Jul 23 2012

%C 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

%C Odd primes p such that -1 is an 8th power mod p. - _Eric M. Schmidt_, Mar 27 2014

%H T. D. Noe, <a href="/A094407/b094407.txt">Table of n, a(n) for n=1..1000</a>

%H C, Caldwell, <a href="https://t5k.org/curios/includes/file.php?file=primetest.html">Prime test</a>.

%H Irving Kaplansky, <a href="http://dx.doi.org/10.1090/S0002-9939-03-07022-9">The forms x+32y^2 and x+64y^2</a>, Proc. Amer. Math. Soc. 131 (2003), 2299-2300

%p 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

%t lst={};Do[p=16*n+1;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2009 *)

%t Select[16*Range[200]+1,PrimeQ] (* _Harvey P. Dale_, Nov 04 2017 *)

%o (Haskell)

%o a094407 n = a094407_list !! (n-1)

%o a094407_list = filter ((== 1) . a010051) [1,17..]

%o -- _Reinhard Zumkeller_, Mar 06 2012

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

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

%K nonn,easy

%O 1,1

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

%E More terms from _Emeric Deutsch_, Dec 23 2004