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

1,2

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.

Links

Table of n, a(n) for n=1..42.

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]

Example

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.

Crossrefs

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

Sequence in context: A095817 A370525 A352413 * A171339 A374619 A032266

Adjacent sequences: A101039 A101040 A101041 * A101043 A101044 A101045

Keyword

nonn

Author

Jens Kruse Andersen, Nov 28 2004

Status

approved