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A007519 Primes of form 8n+1, that is, primes congruent to 1 mod 8.
(Formerly M5037)
69
17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641, 673, 761, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049, 1097, 1129, 1153, 1193, 1201, 1217, 1249, 1289, 1297, 1321, 1361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Integers n (n>9) of form 4k+1 such that binomial(n-1,(n-1)/4) == 1 (mod n) - Benoit Cloitre, Feb 07 2004

Primes of the form x^2+8y^2. - T. D. Noe, May 07 2005

Also primes of the form x^2+16y^2. See A140633. - T. D. Noe, May 19 2008

Is this the same sequence as A141174?

See also remarks in A141174. Being a subset of A001132, this is also a subset of the primes of the form u^2-2*v^2. - Tito Piezas III, Dec 28 2008

These primes p are only which possess the property: for every integer m from interval [0,p)  with the Hamming  distance D(m,p)=2, there exists an integer h from (m,p)  with D(m,h)=2. - Vladimir Shevelev,  Apr 18 2012

Primes p such that p XOR 6 = p + 6. [Brad Clardy, Jul 22 2012]

Odd primes p such that -1 is a 4th power mod p. - Eric M. Schmidt, Mar 27 2014

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

EXAMPLE

a(1)=17=(10001)_2.  All numbers m from [0,17) with the Hamming distance D(m,17)=2 are 0,3,5,9. For m=0, we can take h=3, since 3 from (0,17) and D(0,3)=2; for m=3, we can take h=5, since 5 from (3,17) and D(3,5)=2; for m=5, we can take h=6, since 6  from (5,17) and D(5,6)=2;  for m=9,  we can take h=10, since 10  from (9,17) and D(9,10)=2. - Vladimir Shevelev, Apr 18 2012

MATHEMATICA

a={}; Do[x=8*n+1; If[PrimeQ[x], AppendTo[a, x]], {n, 10^2}]; a - Vladimir Joseph Stephan Orlovsky, Apr 29 2008

Select[1 + 8 Range@ 170, PrimeQ] (* Robert G. Wilson v *)

PROG

(PARI) forprime(p=2, 1e4, if(p%8==1, print1(p", "))) \\ Charles R Greathouse IV, Jun 16 2011

(Haskell)

a007519 n = a007519_list !! (n-1)

a007519_list = filter ((== 1) . a010051) [1, 9..]

-- Reinhard Zumkeller, Mar 06 2012

(MAGMA) [p: p in PrimesUpTo(2000) | p mod 8 eq 1 ]; // Vincenzo Librandi, Aug 21 2912

CROSSREFS

Cf. A139643. Complement in primes of A154264. Cf. A042987.

Cf. A065091, A002144, A094407, A133870, A142925, A208177, A208178, A076339.

Subsequence of A017077.

Sequence in context: A172280 A004625 A141174 * A163185 A138005 A166147

Adjacent sequences:  A007516 A007517 A007518 * A007520 A007521 A007522

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified April 18 10:50 EDT 2014. Contains 240707 sequences.