A218493 First number beginning the smallest chain of n consecutive odd divisors, with no even divisor between, of some factorial s!.

1, 25, 115, 1001, 4429, 7657, 34365, 49375

Offset

1,2

Comments

Minimal values of s are: 1, 10, 23, 67, 211, 163, 157, 163.

The chains are:

1

25, 27

115, 117, 119

1001, 1003, 1005, 1007

4429, 4431, 4433, 4437, 4439

7657, 7659, 7661, 7663, 7665, 7667

34365, 34371, 34375, 34383, 34385, 34391, 34397

49375, 49377, 49379, 49381, 49383, 49385, 49387, 49389

Links

Table of n, a(n) for n=1..8.

Example

The chain for n = 2 is smallest for s = 10 to s = 12.
The chain for n = 3 is smallest for s = 23 to s = 28.
The chain for n = 4 is smallest for s = 67 to s = 166.
The chain for n = 5 is smallest for s = 211 to s = 276.
The chain for n = 6 is smallest for s = 163 to s = 382.
The chain for n = 7 is smallest for s = 157 to s = 178.
The chain for n = 8 is smallest for s = 163 to s = 822.
Note that for n > 2, the range of s starts with a prime number and ends just before a prime number.

Mathematica

n = 4; s = 1; mn = Infinity; While[s < mn, s++; f = s!; consec = 0; lst = {}; i = 1; found = False; While[If[Mod[f, i] == 0, If[OddQ[i], consec++; AppendTo[lst, i]; If[consec == n, found = True], consec = 0; lst = {}]]; ! found && i < mn && i^n < f, i++]; If[found, Print[{s, lst}]; mn = Min[mn, i]]] (* T. D. Noe, Oct 31 2012 *)

Crossrefs

Sequence in context: A340123 A247683 A020152 * A360511 A124953 A126412

Adjacent sequences: A218490 A218491 A218492 * A218494 A218495 A218496

Keyword

nonn

Author

Robin Garcia, Oct 30 2012

Extensions

a(4) and a(5) corrected and a(6) added by T. D. Noe, Oct 31 2012

a(7) and a(8) added by T. D. Noe, Nov 01 2012

Status

approved