A278404 Greater number in the least prime-semiprime gap of size n.

3, 9, 29, 101, 346, 247, 6098, 3181, 2878, 2531, 16033, 26615, 114371, 41793, 74506, 39359, 463178, 104677, 248426, 517441, 923743, 506531, 1930846, 584237, 2560202, 4036993, 4570438, 4552391, 7879282, 4417843, 27841082, 5167619, 13683067, 9725141, 47735377, 25045807, 63305698

Offset: 1

Author

Bobby Jacobs, Charles R Greathouse IV, Jonathan Vos Post, and Robert G. Wilson v, Nov 20 2016

Keywords

• nonn

Comments

A prime-semiprime gap of n is defined as the difference between p & q, p being either a prime, A000040, or a semiprime, A001358, and q being the next greater prime or semiprime, see examples.

The corresponding numbers at the start of the prime-semiprime gaps, i.e., a(n)-n, are in A278351.

Examples

			a(1) = 3 since there is a gap of 1 between 2 and 3, both of which are primes.
a(2) = 9 since there is a gap of 2 between 7 and 9, the first is a prime and the second is a semiprime.
a(3) = 29 since there is a gap of 3 between 26, a semiprime, and 29, a prime.
a(6) = 247 because the first prime-semiprime gap of size 6 is between 241 and 247.
		

Links

• Bobby Jacobs, Charles R Greathouse IV, Jonathan Vos Post, and Robert G. Wilson v, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A037143, A275013, A275014, A275108, A278351.