A212502 Composite numbers k that divide the imaginary part of (1+2i)^A201629(k).

4, 8, 12, 16, 24, 32, 36, 48, 56, 64, 72, 96, 108, 112, 128, 132, 143, 144, 156, 168, 192, 216, 224, 256, 264, 272, 288, 312, 324, 336, 384, 392, 396, 399, 432, 448, 468, 496, 504, 512, 527, 528, 544, 552, 576, 624, 648, 672, 768, 779, 784, 792, 816, 864

Offset: 1

Author

José María Grau Ribas, May 19 2012

Keywords

• nonn

Comments

If p is a prime number then p divides the imaginary part of (1+2i)^A201629(p).

The numbers of this sequence may be called Fermat pseudoprimes to base 1+2i.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Jose María Grau, A. M. Oller-Marcen, Manuel Rodriguez and D. Sadornil, Fermat test with Gaussian base and Gaussian pseudoprimes, arXiv:1401.4708 [math.NT], 2014.

Crossrefs

Cf. A201629, A213337, A212601.

Programs

Maple

A201629:= proc(n) if n::even then n elif n mod 4 = 1 then n-1 else n+1 fi end proc:
filter:= proc(n) not isprime(n) and type(Powmod(1+2*x, A201629(n), x^2+1, x) mod n, integer) end proc:
select(filter, [$2..1000]); # Robert Israel, Nov 06 2019

Mathematica

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 &]

Extensions

Definition revised by José María Grau Ribas, Oct 12 2013