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.

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

Author

Vladimir Shevelev, May 10 2010

Keywords

• nonn

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

• Vladimir Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236.

Crossrefs

Cf. A000142, A177458, A177459, A177355, A177349, A177378, A177436, A050376, A168655, A169661.

Programs

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 *)

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).

Extensions

Extended by T. D. Noe, Apr 10 2012