

A049300


Smallest number which begins the maximal number of consecutive integers divisible by one of the first n prime numbers.


2



2, 2, 2, 2, 114, 9440, 217128, 60044, 20332472, 417086648, 74959204292, 187219155594, 79622514581574, 14478292443584, 6002108856728918, 12288083384384462, 5814429911995661690, 14719192159220252523420
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OFFSET

1,1


COMMENTS

The length of these chains is given by the first maximal gaps minus 1 in reduced residue systems of consecutive primorial numbers: 1,1,3,5,9,13,21,25, etc. (A048670  1).
Let j(m) be the Jacobsthal function (A048669): maximal distance between integers relatively prime to m. Let m=2*3*5*...*prime(n). Then a(n) is the least k>0 such that k,k+1,k+2,...k+j(m)2 are not coprime to m. Note that a(n) begins (or is inside) a large gap between primes.  T. D. Noe, Mar 29 2007


LINKS

Max Alekseyev, Table of n, a(n) for n=1..24 [From Max Alekseyev, Nov 15 2009]


FORMULA

One of prime(1), ..., prime(n) divides a maximal number of consecutive integers starting with a(n), which is minimal of this property.
a(n)=1+A128707(A002110(n))  T. D. Noe, Mar 29 2007


EXAMPLE

Between 1 and 7, all 5 numbers (2,3,4,5,6) are divisible either by 2,3 or 5. Thus a(3)=2, the initial term. Between 113 and 127 the 13 consecutive integers are divisible by 2,5,2,3,2,7,2,11,2,3,2,5,2, each from {2,3,5,7,11}. Thus a(5)=114, the smallest with this property.


CROSSREFS

Cf. A002110, A048670.
Sequence in context: A084954 A226281 A217993 * A084957 A235812 A035307
Adjacent sequences: A049297 A049298 A049299 * A049301 A049302 A049303


KEYWORD

hard,nonn


AUTHOR

Labos Elemer


EXTENSIONS

More terms from T. D. Noe, Mar 29 2007
a(11)a(12) from Donovan Johnson, Oct 13 2009
a(13) from Donovan Johnson, Oct 20 2009
Terms a(14) onwards from Max Alekseyev, Nov 14 2009


STATUS

approved



