OFFSET
1,2
COMMENTS
a(n) is the lengths of n-th row of the table below. Table of numbers k such that (2n+1)!! - 2^k is prime: {0}, {1,2,3}, {1,2,3,4,5,6}, {2,3,4,6,9}, {2,6,7,8,9,10,12,13}, {2,4,7,11,13,14,15}, {1,2,8,11,16,18,20}, {1,4,6,10,12,16,18,19,22,23,24},...
EXAMPLE
a(1) = 1 because there is only one prime of the form 3!! - 2^k = 3!! - 2^0 = 2.
a(2) = 3 because there are three primes of the form 5!! - 2^k: 5!! - 2^1 = 13, 5!! - 2^2 = 11 and 5!! - 2^3 = 7.
MATHEMATICA
Table[Length[Select[Range[0, Floor[Log[2, (2n+1)!! ]]], PrimeQ[(2n+1)!!-2^# ]&]], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Nov 17 2006
STATUS
approved