

A007520


Primes == 3 (mod 8).
(Formerly M2882)


25



3, 11, 19, 43, 59, 67, 83, 107, 131, 139, 163, 179, 211, 227, 251, 283, 307, 331, 347, 379, 419, 443, 467, 491, 499, 523, 547, 563, 571, 587, 619, 643, 659, 683, 691, 739, 787, 811, 827, 859, 883, 907, 947, 971, 1019, 1051, 1091, 1123, 1163, 1171, 1187
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OFFSET

1,1


COMMENTS

Primes of the form 3x^2 + 2xy + 3y^2 with x and y in Z.  T. D. Noe, May 07 2005
Also, primes of the form X^2 + 2Y^2, X=xy, Y=x+y.  Moshe Levin, Dec 06 2011
Each term is the sum of no fewer than three positive squares.  T. D. Noe, Nov 15 2010
Smallest terms expressible as sum of three distinct positive squares: 59=1^2+3^2+7^2, 83=3^2+5^2+7^2, 107, 131, 139, 179, 211, 227, 251, 283, 307.  Moshe Levin, Dec 06 2011


REFERENCES

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].


MATHEMATICA

lst={}; Do[p=8*n+3; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 22 2008 *)
p=3; k=0; nn=1000; Reap[While[k<nn, If[PrimeQ[p], k++; Sow[p]]; p=p+8]][[2, 1]] (* Moshe Levin, Dec 06 2011 *)


PROG

(PARI) forprime(p=2, 97, if(p%8==3, print1(p", "))) \\ Charles R Greathouse IV, Aug 17 2011
(MAGMA) [p: p in PrimesUpTo(2000)  p mod 8 eq 3]; // Vincenzo Librandi, Aug 07 2012


CROSSREFS

Sequence in context: A079544 A192717 A163183 * A213891 A163851 A213051
Adjacent sequences: A007517 A007518 A007519 * A007521 A007522 A007523


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



