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

3,1

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

Table of n, a(n) for n=3..49.

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 *)

Crossrefs

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

Sequence in context: A267646 A264424 A039610 * A157429 A200470 A128676

Adjacent sequences: A177495 A177496 A177497 * A177499 A177500 A177501

Keyword

nonn

Author

Vladimir Shevelev, May 10 2010

Extensions

Extended by T. D. Noe, Apr 10 2012

Status

approved