A249051 The smallest integer > 1 of exactly n consecutive integers divisible respectively by the first n natural numbers (A000027), or 0 if no such number exists.

2, 3, 7, 13, 0, 61, 421, 841, 0, 2521, 0, 27721, 0, 0, 360361, 720721, 0, 12252241, 0, 0, 0, 232792561, 0, 5354228881, 0, 26771144401, 0, 80313433201, 0, 2329089562801, 72201776446801, 0, 0, 0, 0, 144403552893601, 0, 0, 0, 5342931457063201, 0

Offset: 1

Author

Robert G. Wilson v, Oct 30 2014

Keywords

• nonn

Comments

For all n > 1 and a(n) # 0, a(n) == 1 (mod p#), where p# are the primorial numbers (A034386).

When a(n) is not 0, a(n) = A075059(n).

a(n) = 0 when n is a member of A080765.

Examples

			a(3) = 7 because the smallest k such that 1|k, 2|k+1, 3|k+2, and 4 does not divide k+3 is 7.
a(4) = 13 because the smallest k such that 1|k, 2|k+1, 3|k+2, 4|k+3, and 5 does not divide k+4 is 13.
		

Crossrefs

Cf. A075059, A034386, A080765.

Programs

Mathematica

f[n_] := Block[{lcm = LCM @@ Range@ n}, If[ lcm == LCM @@ Range[n + 1], 0, lcm + 1]]; Array[ f, 42] (* Robert G. Wilson v, Nov 13 2014 *)

Extensions

a(5) corrected (0, not 181) by Jon Perry, Nov 05 2014

Sequence corrected by Robert G. Wilson v, Nov 13 2014