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A027206 Numbers n such that (1+i)^n + i is a Gaussian prime. 3
0, 1, 2, 3, 4, 6, 7, 8, 11, 14, 16, 19, 38, 47, 62, 79, 151, 163, 167, 214, 239, 254, 283, 367, 379, 1214, 1367, 2558, 4406, 8846, 14699, 49207, 77291, 160423, 172486, 221006, 432182, 1513678, 2515574 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently, either (1+i)^n + i times its conjugate is an ordinary prime, or n == 2 (mod 4) and 2^(n/2) + (-1)^((n-2)/4) is an ordinary prime.

Let z = (1+i)^n + i. If z is not pure real or pure imaginary, then z is a Gaussian prime if the product of z and its conjugate is a rational prime. That product is 1 + 2^n + sin(n*Pi/4)*2^(1+n/2). z is imaginary when n=4k+2, in which case, z has magnitude 2^(2k+1) + (-1)^k. These pure imaginary numbers are Gaussian primes when 2^(2k+1)-1 is a Mersenne prime and 2k+1 = 1 (mod 4); that is, when n is twice an odd number in A112633. - T. D. Noe, Mar 07 2011

LINKS

Table of n, a(n) for n=1..39.

Index entries for Gaussian integers and primes

MATHEMATICA

Select[Range[0, 30000], PrimeQ[(1+I)^#+I, GaussianIntegers->True]&]

CROSSREFS

Cf. A057429, A103329.

Sequence in context: A102826 A191381 A163866 * A198034 A016027 A265347

Adjacent sequences:  A027203 A027204 A027205 * A027207 A027208 A027209

KEYWORD

nonn

AUTHOR

Ed Pegg Jr, Aug 07 2002

EXTENSIONS

More terms from Mike Oakes, Aug 07 2002

Edited by Dean Hickerson, Aug 14 2002

0 prepended by T. D. Noe, Mar 07 2011

STATUS

approved

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Last modified March 20 09:50 EDT 2019. Contains 321345 sequences. (Running on oeis4.)