This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049300 Smallest number starting a longest interval of consecutive integers, each of which is divisible by at least one of the first n primes. 2
2, 2, 2, 2, 114, 9440, 217128, 60044, 20332472, 417086648, 74959204292, 187219155594, 79622514581574, 14478292443584, 6002108856728918, 12288083384384462, 5814429911995661690, 14719192159220252523420 (list; graph; refs; listen; history; text; internal format)



The length of such longest interval of consecutive integers is given by A058989(n), which is the first maximal gaps A048670(n) minus 1 in the reduced residue system of consecutive primorial numbers.

Let j(m)=A048669(m) be the Jacobsthal function, i.e., the 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


Max Alekseyev, Table of n, a(n) for n = 1..24


a(n) = 1 + A128707(A002110(n)). - T. D. Noe, Mar 29 2007


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.


Cf. A002110, A048670.

Sequence in context: A084954 A226281 A217993 * A084957 A239944 A235812

Adjacent sequences:  A049297 A049298 A049299 * A049301 A049302 A049303




Labos Elemer


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)-a(24) from Max Alekseyev, Nov 14 2009



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 4 09:05 EST 2016. Contains 278749 sequences.