cp's OEIS Frontend

A094407 Primes of the form 16n+1.

%I A094407 #42 Apr 03 2023 10:36:10
%S A094407 17,97,113,193,241,257,337,353,401,433,449,577,593,641,673,769,881,
%T A094407 929,977,1009,1153,1201,1217,1249,1297,1361,1409,1489,1553,1601,1697,
%U A094407 1777,1873,1889,2017,2081,2113,2129,2161,2273,2417,2593,2609,2657,2689,2753
%N A094407 Primes of the form 16n+1.
%C A094407 Subsequence of A007519 (primes of form 8n+1). - _Zak Seidov_, May 16 2012
%C A094407 Primes p such that p XOR 14 = p + 14. - _Brad Clardy_, Jul 23 2012
%C A094407 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 A094407 Odd primes p such that -1 is an 8th power mod p. - _Eric M. Schmidt_, Mar 27 2014
%H A094407 T. D. Noe, <a href="/A094407/b094407.txt">Table of n, a(n) for n=1..1000</a>
%H A094407 C, Caldwell, <a href="https://t5k.org/curios/includes/file.php?file=primetest.html">Prime test</a>.
%H A094407 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 A094407 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 A094407 lst={};Do[p=16*n+1;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2009 *)
%t A094407 Select[16*Range[200]+1,PrimeQ] (* _Harvey P. Dale_, Nov 04 2017 *)
%o A094407 (Haskell)
%o A094407 a094407 n = a094407_list !! (n-1)
%o A094407 a094407_list = filter ((== 1) . a010051) [1,17..]
%o A094407 -- _Reinhard Zumkeller_, Mar 06 2012
%Y A094407 Primes congruent to k mod 16: A094407, A091968, A127589, A141194, A105126, A141195, A141196, A127576.
%Y A094407 Cf. A065091, A002144, A007519, A133870, A142925, A208177, A208178, A076339.
%K A094407 nonn,easy
%O A094407 1,1
%A A094407 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jun 03 2004
%E A094407 More terms from _Emeric Deutsch_, Dec 23 2004