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%I #37 Sep 08 2022 08:45:32
%S 97,193,257,353,449,577,641,673,769,929,1153,1217,1249,1409,1601,1697,
%T 1889,2017,2081,2113,2273,2593,2657,2689,2753,3041,3137,3169,3329,
%U 3361,3457,3617,4001,4129,4289,4481,4513,4673,4801,4993,5153,5281,5441,5569
%N Primes of the form 32*n + 1.
%C Corresponding n's: 3, 6, 8, 11, 14, 18, 20, 21, 24, 29, 36, 38, 39, ... (A133869).
%C These primes p are the only ones with the property that for every integer m from interval [0,p) with the Hamming distance D(m,p) = 2 or 3, there exists an integer h from (m,p) with D(m,h) = D(m,p). - _Vladimir Shevelev_, Apr 19 2012
%C Primes p such that p XOR 30 = p + 30. - _Brad Clardy_, Jul 22 2012
%C Odd primes p such that -1 is a 16th power mod p. - _Eric M. Schmidt_, Mar 27 2014
%H Reinhard Zumkeller, <a href="/A133870/b133870.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[32*Range[175] + 1, PrimeQ] (* _Alonso del Arte_, Jul 24 2012 *)
%t Select[Prime[Range[4000]],MemberQ[{1},Mod[#,32]]&] (* _Vincenzo Librandi_, Aug 18 2012 *)
%o (Haskell)
%o a133870 n = a133870_list !! (n-1)
%o a133870_list = filter ((== 1) . a010051) [1,33..]
%o -- _Reinhard Zumkeller_, Mar 06 2012
%o (Magma) [p: p in PrimesUpTo(12000) | p mod 32 eq 1 ]; // _Vincenzo Librandi_, Aug 18 2012
%Y Cf. A000040, A133869; A065091, A002144, A007519, A094407, A142925, A208177, A208178, A076339.
%K nonn,easy
%O 1,1
%A _Zak Seidov_, Sep 27 2007
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