A123688 a(n) = number of primes of the form (2n+1)!! - 2^k.

1, 3, 6, 5, 8, 7, 7, 11, 8, 9, 9, 12, 7, 11, 12, 11, 16, 8, 13, 12, 13, 16, 8, 7, 8, 8, 12, 6, 8, 14, 13, 5, 16, 13, 11, 19, 16, 8, 20, 19, 15, 11, 12, 13, 7, 9, 8, 9, 14, 6, 12, 11, 13, 20, 18, 13, 9, 12, 14, 13, 14, 11, 13, 14, 13, 13, 16, 13, 10, 10, 17, 20, 10, 13, 10, 20, 11, 19, 17

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},...

Links

Table of n, a(n) for n=1..79.

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

Sequence in context: A113533 A330525 A201418 * A082284 A241474 A259556

Adjacent sequences: A123685 A123686 A123687 * A123689 A123690 A123691

Keyword

nonn

Author

Alexander Adamchuk, Nov 17 2006

Status

approved