login
A177498
a(n) is the maximal positive integer m for which exponents of prime(n) and prime(n+1) in the prime power factorization of m! are both powers of 2.
4
20, 98, 54, 38, 152, 94, 68, 260, 154, 332, 696, 386, 234, 476, 1002, 548, 1138, 2342, 656, 1342, 746, 800, 1648, 3332, 1750, 3530, 1852, 1016, 2158, 2226, 8904, 1250, 9684, 2566, 2668, 5378, 2838, 2940, 11634, 3076, 12414, 6368, 12804, 3382, 3586, 7358, 14754
OFFSET
3,1
COMMENTS
For n=2 the corresponding value is not known; moreover, we do not know if this value is finite (in any case, it is not less than 524306). See also comment to A177458.
If a(2) exists, then it is at least 81129638414606681695789005144146. - Charles R Greathouse IV, Apr 10 2012
LINKS
V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236.
FORMULA
The maximal m with the considered property is in interval [q, 2*(-1+q^2*(log(2)/(2*log(q)-1)+1))), where q=prime(n+1).
MATHEMATICA
tp[n_] := Flatten[Position[FoldList[Plus, 0, IntegerExponent[Range[100000], n]], _?(IntegerQ[Log[2, #]] &)]]; Table[s = Intersection[tp[Prime[n]], tp[Prime[n + 1]]] - 1; s[[-1]], {n, 3, 60}] (* T. D. Noe, Apr 10 2012 *)
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 10 2010
EXTENSIONS
Extended by T. D. Noe, Apr 10 2012
STATUS
approved