A180100 a(n) = smallest number k such that five consecutive prime numbers prime(n), prime(n+1), prime(n+2), prime(n+3) and prime(n+4) are divisors of k, k+1, k+2, k+3, and k+4 respectively.

788, 789, 40830, 142933, 420068, 709800, 4372298, 1229395, 16530376, 21985509, 28051993, 70973992, 185156451, 330508793, 133276396, 273856936, 1164119973, 994656606, 912355750, 640476303, 3366929360, 706420054, 4180201127

Offset

1,1

Links

Table of n, a(n) for n=1..23.

Example

a(8) = 1229395 as prime(8) = 19 =>
  1229395 = 19*64705 ;
  1229396 = 23*53452 ;
  1229397 = 29*42393 ;
  1229398 = 31*39658 ;
  1229399 = 37*33227.

Maple

with(numtheory):for p from 1 to 50 do: p1:=ithprime(p):p2:=ithprime(p+1):p3:=ithprime(p+2):p4:=ithprime(p+3):p5:=ithprime(p+4):it:=0:for   n from 1 to 5000000 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 then it:=1:printf(`%d, `, n):else fi:od:od:

Prog

(Sage) def A180100(n): return crt([-4..0][::-1], [nth_prime(i) for i in [n..n+4]]) # D. S. McNeil, Jan 16 2011

Crossrefs

Cf. A077338 A180095 A180096.

Sequence in context: A097775 A321210 A072730 * A072722 A180159 A207280

Adjacent sequences: A180097 A180098 A180099 * A180101 A180102 A180103

Keyword

nonn

Author

Michel Lagneau, Jan 16 2011

Status

approved