A107257 Smallest prime p such that for each j <= n there are primes a < b <= p whose difference b - a is 2*j.

5, 7, 11, 11, 13, 17, 17, 19, 23, 23, 29, 29, 29, 31, 37, 37, 37, 41, 41, 43, 47, 47, 53, 53, 53, 59, 59, 59, 61, 67, 67, 67, 71, 71, 73, 79, 79, 79, 83, 83, 89, 89, 89, 101, 101, 101, 101, 101, 101, 103, 107, 107, 109, 113, 113, 131, 131, 131, 131, 131, 131, 131, 131

Offset: 1

Author

Klaus Brockhaus, May 15 2005

Keywords

• nonn

Comments

Every positive even number <= 2*n is the difference of two suitable primes <= a(n).

Sequence is nondecreasing, whereas the related sequence A020484 is not; first divergence is at 45: a(45) = 101, A020484(45) = 97.

Examples

			Consider n = 45: 89, 97, 101 are consecutive primes, 2*45 = 97 - 7, but 2*44 = 101 - 13 cannot be written as b - a where a and b are primes <=97, hence a(45) = 101.
		

Crossrefs

Cf. A060264, A020484.