OFFSET
3,1
COMMENTS
This gives the number of rows in A115627 for which the n-th and (n+1)st column are both in {1,2,4,8,16,..}.
For n=2 the corresponding value is not known and >=25; moreover, we do not know if this value is finite.
A more general result concerning the cases for non-adjacent primes and a finite search interval for the values of m is in the 2007 publication.
LINKS
V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236.
EXAMPLE
For n=3, the 9 values of m are 7, 8, 9, 10, 11, 12, 13, 14, and 20.
m=6, for example, is not counted because 6!=2^4*3^2*5 does not contain prime(4)=7.
m=15, for example, is not counted because 15!=2^11*3^6*5^3*7^2*11*13 contains a third power of prime(3)=5.
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; Length[s], {n, 3, 60}] (* T. D. Noe, Apr 10 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, May 09 2010, May 10 2010
EXTENSIONS
Edited, example and relation to A115627 added, terms after 120 added - R. J. Mathar, Oct 29 2010
Extended by T. D. Noe, Apr 10 2012
STATUS
approved