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A218493
First number beginning the smallest chain of n consecutive odd divisors, with no even divisor between, of some factorial s!.
1
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
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
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