A113593 Minimal differences that appear in arithmetic progressions of primes.

0, 1, 2, 6, 30, 150, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230

Offset: 1

Author

Jon Wild, Jan 26 2006

Keywords

• nonn

Comments

Collapsed version of sequence A033188. If a conjecture about arithmetic prime progressions is correct (see A033188), this sequence is simply the primorial numbers with 150 inserted into the list. Zero is also included (since p,p is an arithmetic progression with difference 0).

Examples

			2 belongs in the sequence because the smallest d satisfying "n, n+d, n+2d are all prime" is 2. 4 does not belong, despite there existing triples {n, n+4, n+8} that are all prime--because a difference of 4 does not allow a new length of progression, i.e. there is no prime progression {n, n+4, n+8, n+12}.
		

Crossrefs

Cf. A033188, A034386, A002110.