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

1,1

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.

Links

Table of n, a(n) for n=1..41.

Example

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.

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 *)

Crossrefs

Cf. A075059, A034386, A080765.

Sequence in context: A084423 A361910 A068134 * A329413 A225093 A278007

Adjacent sequences: A249048 A249049 A249050 * A249052 A249053 A249054

Keyword

nonn

Author

Robert G. Wilson v, Oct 30 2014

Extensions

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

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

Status

approved