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 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)



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


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


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


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) onwards from Max Alekseyev, Nov 14 2009



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

Content is available under The OEIS End-User License Agreement .

Last modified December 1 22:15 EST 2015. Contains 264709 sequences.