A209834 a(A074773(n) mod 1519829 mod 18) = A074773(n), 1 <= n <= 18.

3343433905957, 1871186716981, 307768373641, 546348519181, 1362242655901, 2273312197621, 354864744877, 3474749660383, 2366338900801, 602248359169, 3215031751, 2152302898747, 315962312077, 457453568161, 528929554561, 3477707481751, 118670087467, 3461715915661

Offset: 0

Author

Washington Bomfim, Mar 14 2012

Keywords

• nonn
• fini
• full

Comments

From the first reference, for numbers up to 10^12 only four strong pseudoprimality tests (with bases 2, 13, 23, 1662803) are necessary for proving primality. Since A074773(19) = 4341937413061, up to 4.10^12 we can use the four bases 2, 3, 5, 7 and if a number n passes the tests, we check if n is equal to a(n mod 1519829 mod 18). If not, n is prime. A unique comparison is used so we have a primality test equally efficient for an interval four times larger. See the Bomfim link.

Terms computed using table by Charles R Greathouse IV. See A074773.

Examples

			A074773(15) mod 1519829 mod 18 = 0, so a(0) = A074773(15).
A074773(11) mod 1519829 mod 18 = 1, so a(1) = A074773(11).
		

Links

• Washington Bomfim, A method to find bijections from a set of n integers to {0,1, ... ,n-1}
• G. Jaeschke, On strong pseudoprimes to several bases, Mathematics of Computation, 61 (1993), 915-926.

Crossrefs

Cf. A074773, A209833.