OFFSET
1,3
COMMENTS
Equivalently, either (1+i)^m + i times its conjugate is an ordinary prime, or m == 2 (mod 4) and 2^(m/2) + (-1)^((m-2)/4) is an ordinary prime.
Let z = (1+i)^m + 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^m + sin(m*Pi/4)*2^(1+m/2). z is imaginary when m=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 m is twice an odd number in A112633. - T. D. Noe, Mar 07 2011
MATHEMATICA
Select[Range[0, 30000], PrimeQ[(1+I)^#+I, GaussianIntegers->True]&]
CROSSREFS
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