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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 (list; graph; refs; listen; history; text; internal format)
 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 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: A050589 A247683 A020152 * A124953 A126412 A078815 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

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)