A180159 a(n) = smallest number k such that six consecutive prime numbers prime(n), prime(n+1),...,prime(n+5) are divisors of k, k+1,..., k+5 respectively.

788, 210999, 466255, 4669455, 25916396, 51122994, 204732428, 204732429, 549769529, 2309049600, 883426096, 5108177043, 2258007227, 15750496273, 22958443910, 11162458684, 41157474821, 32790221027, 130700807239

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(4)= 4669455 because prime(4) = 7 =>
  4669455 = 7*667065  ;
  4669456 = 11*424496 ;
  4669457 = 13*359189 ;
  4669458 = 17*274674 ;
  4669459 = 19*245761 ;
  4669460 = 23*203020.

Maple

with(numtheory):for p from 1 to 15 do: p1:=ithprime(p):p2:=ithprime(p+1):p3:=ithprime(p+2):p4:=ithprime(p+3):p5:=ithprime(p+4):p6:=ithprime(p+5):it:=0:for
  n from 1 to 50000000 while(it=0) do:if irem(n, p1)=0 and irem(n+1, p2)=0 and
  irem(n+2, p3)=0 and irem(n+3, p4)=0 and irem(n+4, p5)=0 and irem(n+5, p6)=0
  then it:=1:printf(`%d, `, n):else fi:od:od:

Prog

(Sage) def A180159(n): return crt([-5..0][::-1], [nth_prime(i) for i in [n..n+5]]) # D. S. McNeil, Jan 16 2011
(PARI) a(n)=my(p=prime(n), r=Mod(0, p)); for(i=1, 5, p=nextprime(p+1); r=chinese(r, Mod(-i, p))); lift(r) \\ Charles R Greathouse IV, Jan 16 2011

Crossrefs

Cf. A077338, A180095, A180096, A180100.

Sequence in context: A072730 A180100 A072722 * A207280 A207476 A207532

Adjacent sequences: A180156 A180157 A180158 * A180160 A180161 A180162

Keyword

nonn

Author

Michel Lagneau, Jan 16 2011

Status

approved