A101042 a(n) is the smallest positive d such that the n-th prime is the smallest prime p for which p+d is also prime.

1, 2, 6, 22, 116, 88, 470, 112, 284, 242, 202, 772, 1326, 718, 1334, 1328, 2558, 1762, 1642, 2402, 3274, 1732, 7094, 9512, 7984, 5246, 12688, 10532, 9952, 16766, 7702, 60458, 9974, 25708, 5888, 13528, 10342, 25678, 62156, 69518, 76838, 37666

Offset: 1

Author

Jens Kruse Andersen, Nov 28 2004

Keywords

• nonn

Comments

Except for n=1, A020483(a(n)/2) is the first appearance of the n-th prime. It is conjectured that a(n) always exists. a(386) is the first number which must be above 10^12.

Examples

			a(3)=6 because: The 3rd prime is 5. 2+6, 3+6 is composite, 5+6 is prime. 6 is the smallest such number.
		

Links

• J. K. Andersen, Prime gaps (not necessarily consecutive).
• Mike Oakes, Ed Pegg Jr, Jens Kruse Andersen, Prime gaps (not necessarily consecutive), digest of 5 messages in primenumbers Yahoo group, Nov 26 - Nov 27, 2004. [Cached copy]

Crossrefs

Cf. A020483, A101043, A101044, A101045, A101046.