A133870 Primes of the form 32*n + 1.

97, 193, 257, 353, 449, 577, 641, 673, 769, 929, 1153, 1217, 1249, 1409, 1601, 1697, 1889, 2017, 2081, 2113, 2273, 2593, 2657, 2689, 2753, 3041, 3137, 3169, 3329, 3361, 3457, 3617, 4001, 4129, 4289, 4481, 4513, 4673, 4801, 4993, 5153, 5281, 5441, 5569

Offset: 1

Author

Zak Seidov, Sep 27 2007

Keywords

• nonn
• easy

Comments

Corresponding n's: 3, 6, 8, 11, 14, 18, 20, 21, 24, 29, 36, 38, 39, ... (A133869).

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

Primes p such that p XOR 30 = p + 30. - Brad Clardy, Jul 22 2012

Odd primes p such that -1 is a 16th power mod p. - Eric M. Schmidt, Mar 27 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A133869; A065091, A002144, A007519, A094407, A142925, A208177, A208178, A076339.

Programs

Haskell

a133870 n = a133870_list !! (n-1)
a133870_list = filter ((== 1) . a010051) [1,33..]
-- Reinhard Zumkeller, Mar 06 2012

Magma

[p: p in PrimesUpTo(12000) | p mod 32 eq 1 ]; // Vincenzo Librandi, Aug 18 2012

Mathematica

Select[32*Range[175] + 1, PrimeQ] (* Alonso del Arte, Jul 24 2012 *)
Select[Prime[Range[4000]],MemberQ[{1},Mod[#,32]]&] (* Vincenzo Librandi, Aug 18 2012 *)