1,1

Primes which are also Gaussian primes.

sin(a(n)*pi/2) = -1 with pi=3.1415..., see A070750. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 04 2002

n such that the product of coefficients of (2n)-th cyclotomic polynomial equals -1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 22 2002

For p and q both belonging to the sequence, exactly one of the congruences x^2=p (mod q), x^2=q (mod p) is solvable, according to Gauss reciprocity law. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 17 2003

Also primes p that divide Lucas[(p-1)/2] or Lucas[(p+1)/2], where Lucas[n] = A000032[n]. Union of A122869 and A122870. - Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 16 2006

Primes which are not the sum of two squares. - Artur Jasinski (grafix(AT)csl.pl), Nov 15 2006

Also odd primes p that divide ((p-1)!! + 1) or ((p-2)!! + 1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 30 2006

Also odd primes p that divide ((p-1)!! - 1) or ((p-2)!! - 1). - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 18 2007

The set of Gaussian primes is a proper subset of the set of the absolute values of negative fundamental discriminants (A003657). - Paul Muljadi (paulmuljadi(AT)yahoo.com), Mar 29 2008

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.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, p. 219, th. 252.

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, December 1972 [alternative scanned copy].

D. Alpern, Gaussian primes

A. Granville and G. Martin, Prime number races

H. J. Smith, Gaussian Primes

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, "Gaussian Integer".

Wolfram Research, The Gauss Reciprocity Law

Index entries for Gaussian integers and primes

Cf. A002144. Apart from initial term, same as A045326.

Cf. A122869, A122870, A000032.

A000040 \setminus A002313

Cf. A003657.

Adjacent sequences: A002142 A002143 A002144 this_sequence A002146 A002147 A002148

Sequence in context: A085760 A131426 A080978 this_sequence A101288 A092109 A117991

nonn,easy

njas

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 21 2000