A143265 a(n) = the smallest integer >= n such that all the distinct primes that divide n and a(n) together are members of a set of consecutive primes. In other words, a(n) is the smallest integer >= n such that n*a(n) is contained in sequence A073491.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 11, 12, 13, 15, 15, 16, 17, 18, 19, 21, 25, 105, 23, 24, 25, 1155, 27, 30, 29, 30, 31, 32, 35, 15015, 35, 36, 37, 255255, 385, 42, 41, 45, 43, 105, 45, 4849845, 47, 48, 49, 51, 5005, 1155, 53, 54, 56, 60, 85085, 111546435, 59, 60, 61

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..4096 (computed from A137795 b-file)

Formula

a(n) = A137795(n) * Ceiling(n/A137795(n)). - Ray Chandler, Nov 09 2008

Example

20 is factored as 2^2 *5^1. Checking the integers >= 20: 20*20 is not factorable into consecutive primes, since 3 is missing. 21 is factored as 3^1 *7^1. Since the distinct primes that divide 20 and 21 (which are 2,3,5,7) form a set of consecutive primes, then a(20) = 21.

Crossrefs

Cf. A073491, A137795.

Sequence in context: A029731 A248899 A029970 * A109841 A174234 A163807

Adjacent sequences: A143262 A143263 A143264 * A143266 A143267 A143268

Keyword

nonn

Author

Leroy Quet, Aug 03 2008

Extensions

Inserted a(15) and a(21) and extended by R. J. Mathar, Aug 14 2008

a(46)-a(61) from Ray Chandler, Nov 09 2008

Status

approved