A106377 Real part of Gaussian prime numbers such that the Gaussian Primorial product up to them is a Gaussian prime minus one.

1, 1, 2, 3, 2, 1, 4, 2, 1, 6, 7, 1, 10, 19, 25

Offset

0,3

Comments

Consider the Gaussian primes of the first quadrant a+bi, with a>0, b>=0, ordered as a sequence by the size of the norm and the size of the real part a, as defined in A103431. The product of these primes up to a+bi, written here as cp#, may have the property that cp#+1 is a Gaussian prime. a(n) is the real part a of such a+bi. cp#+1 is not necessarily in the first quadrant.

Consider the partial products of the complex sequence A103431(n)+A103432(n)*i, which starts p# = 1+i, -1+3i, -5+5i, -15+15i, -75-15i, -195-195i, 585-975i, 3315-3315i,.. If 1+p# is a Gaussian prime, we insert the real part of the last factor, A103431(n), into this sequence. The first missing element is A103431(6), meaning -194-195i is not a Gaussian prime. - R. J. Mathar, Jun 13 2011

The 7 is for products up to norm 192, the 1 for products up to 256, the 10 for 268, 19 up to 360 and the 25 up to 820. (No further up to norm 5700. Is the sequence finite?) - R. J. Mathar, Jun 13 2011

Links

Table of n, a(n) for n=0..14.

Sven Simon, List for A106377/A106378

Example

(1+i)*(1+2i)*(2+i)*3*(2+3i) + 1 = (-75-15i) + 1 = (-74-15i), which is a Gaussian prime. This is the 5th number with the property, so a(5) = 2.

Crossrefs

Cf. A103431, A103432, A106378, A106379, A106381, A106383.

Sequence in context: A231725 A106559 A280047 * A214573 A344090 A344092

Adjacent sequences: A106374 A106375 A106376 * A106378 A106379 A106380

Keyword

nonn,more

Author

Sven Simon, Apr 30 2005

Status

approved