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%I #51 Feb 18 2021 00:45:58
%S 4,8,12,16,24,32,36,48,56,64,72,96,108,112,128,132,143,144,156,168,
%T 192,216,224,256,264,272,288,312,324,336,384,392,396,399,432,448,468,
%U 496,504,512,527,528,544,552,576,624,648,672,768,779,784,792,816,864
%N Composite numbers k that divide the imaginary part of (1+2i)^A201629(k).
%C If p is a prime number then p divides the imaginary part of (1+2i)^A201629(p).
%C The numbers of this sequence may be called Fermat pseudoprimes to base 1+2i.
%H Robert Israel, <a href="/A212502/b212502.txt">Table of n, a(n) for n = 1..10000</a>
%H Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, <a href="http://arxiv.org/abs/1401.4708">Fermat test with Gaussian base and Gaussian pseudoprimes</a>, arXiv:1401.4708 [math.NT], 2014.
%p A201629:= proc(n) if n::even then n elif n mod 4 = 1 then n-1 else n+1 fi end proc:
%p filter:= proc(n) not isprime(n) and type(Powmod(1+2*x, A201629(n), x^2+1, x) mod n, integer) end proc:
%p select(filter, [$2..1000]); # _Robert Israel_, Nov 06 2019
%t A201629[n_]:=Which[Mod[n,4]==3,n+1,Mod[n,4]==1,n-1,True,n]; Select[1+ Range[1000], ! PrimeQ[#] && Im[PowerMod[1 + 2I, A201629[#], #]] == 0 &]
%Y Cf. A201629, A213337, A212601.
%K nonn
%O 1,1
%A _José María Grau Ribas_, May 19 2012
%E Definition revised by _José María Grau Ribas_, Oct 12 2013