Search: id:A057429
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%I A057429
%S A057429 2,3,5,7,11,19,29,47,73,79,113,151,157,163,167,239,241,283,353,367,379,
%T A057429 457,997,1367,3041,10141,14699,27529,49207,77291,85237,106693,160423,
%U A057429 203789,364289,991961
%N A057429 Gaussian-Mersenne primes: numbers n such that (1+i)^n - 1 times its conjugate 
               is prime.
%C A057429 Equivalently, numbers n such that (1+i)^n - 1 is a Gaussian prime.
%C A057429 Note that n must be a rational prime. Also note that (1+i)^n+i or (1+i)^n-i 
               is also a Gaussian prime. - T. D. Noe (noe(AT)sspectra.com), Jan 
               31 2005
%D A057429 Mike Oakes, posting to the Mersenne list, Sep 07 2000.
%H A057429 C. Caldwell, <a href="http://primes.utm.edu/primes/download.php">The 
               largest known primes</a>
%H A057429 Marc Chamberland, <a href="http://www.cs.uwaterloo.ca/journals/JIS/">
               Binary BBP-Formulae for Logarithms...</a>, J. Integer Seqs., Vol. 
               6, 2003.
%H A057429 M. Oakes, <a href="http://www.mail-archive.com/mersenne@base.com/msg05162.html">
               A new series of Mersenne-like Gaussian primes</a>
%H A057429 M. Oakes, <a href="http://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0512&L=nmbrthry&T=0&F=&S=&P=2997">
               Posting to the Number Theory list</a>, Dec 27 2005
%H A057429 <a href="Sindx_Ga.html#gaussians">Index entries for Gaussian integers 
               and primes</a>
%e A057429 Note that 4 is not in the sequence because (1+i)^4 - 1 = -5, which is 
               an integer prime, but not a Gaussian prime.
%t A057429 Do[a = (1 + I)^n - 1; b = a*Conjugate[a]; If[PrimeQ[b], Print[n]], {n, 
               1, 160426}]
%Y A057429 Cf. A000043, A066408, A007670, A007671, A027206.
%Y A057429 Cf. A027206 ((1+i)^n + i is a Gaussian prime), A103329 ((1+i)^n - i is 
               a Gaussian prime).
%Y A057429 Sequence in context: A039726 A115617 A003064 this_sequence A065726 A118985 
               A089769
%Y A057429 Adjacent sequences: A057426 A057427 A057428 this_sequence A057430 A057431 
               A057432
%K A057429 nonn,nice,hard
%O A057429 1,1
%A A057429 Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 07 2000
%E A057429 364289 found by Nicholas Glover on Jun 02 2001 - Mike Oakes (mikeoakes2(AT)aol.com)
%E A057429 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 14 2002; 
               revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 28 2005

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