A180095 a(n) = smallest number k such that three consecutive prime numbers prime(n), prime(n+1) and prime(n+2) are divisors of k, k+1 and k+2 respectively.

8, 54, 20, 791, 1936, 169, 4046, 114, 9453, 31929, 23901, 2664, 44977, 65188, 122482, 134991, 170982, 220027, 101103, 85555, 27886, 296724, 629140, 154326, 546207, 46864, 950587, 1043892, 1548890, 70738, 702945, 2389964

Offset

1,1

Links

Marius A. Burtea, Table of n, a(n) for n = 1..1227

Example

a(20) = 85555 is a term because prime(20) = 71 => 85555 = 71*1205 ; 85556 =
  73*1172 and 85557 = 79*1083 where 71, 73 and 79 are three consecutive primes.

Maple

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

Mathematica

snk[n_]:=Module[{k=1}, While[!AllTrue[{k, k+1, k+2}/n, IntegerQ], k++]; k]; snk/@Partition[Prime[Range[35]], 3, 1] (* Harvey P. Dale, Feb 26 2015 *)

Prog

(Sage) def A180095(n): return crt([-2..0][::-1], [nth_prime(i) for i in [n..n+2]]) # D. S. McNeil, Jan 16 2011

Crossrefs

Cf. A077338.

Sequence in context: A337554 A370359 A070928 * A234955 A189393 A350236

Adjacent sequences: A180092 A180093 A180094 * A180096 A180097 A180098

Keyword

nonn

Author

Michel Lagneau, Jan 16 2011

Status

approved