A214500 The size of the set of numbers k>=0 such that all (3^n+k)*3^n-1 are prime but only the last (largest) (3^n+k)*3^n+1 is also an associated twin prime.

1, 2, 1, 2, 3, 3, 9, 3, 4, 1, 8, 20, 4, 10, 24, 8, 17, 9, 28, 16, 19, 6, 33, 19, 12, 5, 49, 27, 25, 26, 10, 91, 143, 9, 41, 14, 36, 11, 34, 26, 28, 10, 50, 7, 12, 11, 8, 27, 13, 4, 44, 138, 50, 10, 45, 21, 51, 84, 65, 48, 39, 139, 36, 19, 22, 85, 113, 105, 5, 36

Offset: 1

Author

Pierre CAMI, Jul 20 2012

Keywords

• nonn

Comments

Starting at a count of zero, we consider for increasing k>=0 the pairs (3^n+k)*3^n+-1. If the smaller of these two numbers is prime, we increase the counter. If the larger of these two numbers is also prime, we admit the counter to the sequence. It is basically a measure of how many unsuccessful primality tests on the larger of the two numbers are done before it becomes a compatible twin prime.

Heuristically, the average of a(n)/n over n=1 to N tends to 0.83 as N increases.

Crossrefs

Cf. A212037, A214495, A214496, A214499.